The investigations by the state’s Department of Family and Protective Services started last week with an employee of the agency, according to the suit, after Gov. Greg Abbott called for such inquiries.HOUSTON — Texas officials have begun investigating parents of transgender adolescents for possible child abuse, according to a lawsuit filed on Tuesday, after Gov. Greg Abbott directed them last week to handle certain medical treatments as possible crimes.The investigations by the state’s Department of Family and Protective Services, which have not been previously reported, were launched in response to an order from Mr. Abbott to the agency, the lawsuit says. The order followed a nonbinding opinion by the Texas attorney general, Ken Paxton, that parents who provide their transgender teenagers with puberty-suppressing drugs or other medically accepted treatments — which doctors describe as gender-affirming care — could be investigated for child abuse.Among the first to be investigated was an employee of the state protective services agency who has a 16-year-old transgender child. On Tuesday, the American Civil Liberties Union of Texas and Lambda Legal went to state court in Austin to try to stop the inquiry.The employee, who was not named in the court filing, works on the review of reports of abuse and neglect. She was placed on administrative leave last week, according to the filing, and on Friday was visited by an investigator from the agency, which is also seeking medical records related to her child. The family of the child, identified in court documents only as Mary Doe, has refused to voluntarily turn over the records.“We are terrified for Mary’s health and well-being, and for our family,” wrote the employee in a declaration filed with the suit, in which she and her husband are identified as Jane and John Doe. “I feel betrayed by my state and the agency for whom I work.”She added: “Not providing Mary with the medically necessary health care that she needs is not an option for us.”A rally against a Texas bill banning transgender student athletes from participating in school sports, outside the Capitol in Austin in October. The law went into effect in January.Jay Janner/Austin American-Statesman, via Associated PressAccording to the lawsuit, the state’s investigator told the parents that the only allegation against them was that their transgender daughter might have been provided with gender-affirming health care and was “currently transitioning from male to female.”A spokeswoman for the state protective agency did not immediately respond to a request for comment.It was not clear that Mr. Abbott’s order would survive judicial scrutiny. They do not change Texas law, and several county attorneys and district attorneys have said that they would not prosecute families for child abuse under the new definition. Still, the directive by Mr. Abbott has had a chilling effect, and the ramifications of the redefinition are significant.As Mr. Abbott described in his letter, the order would mean that “all licensed professionals who have direct contact with children” would be required to report to state authorities those that they believe are receiving gender-affirming treatment, or face criminal penalties.In the court filing on Tuesday, the A.C.L.U. of Texas and Lambda Legal, a civil rights organization focusing on the L.G.B.T.Q. community, sought to block the request for medical records in the employee’s case and, more broadly, challenged the legitimacy of the investigation and the power of the governor to change the definition of child abuse. According to the filing, other investigations have also begun.The groups argue in the suit that the directive by the governor was issued improperly under state law, ran afoul of the Texas constitution and violated the constitutional rights of transgender youth, as well as their parents.“No family should have to fear being torn apart because they are supporting their trans child,” Adri Pérez, the policy strategist at the A.C.L.U. of Texas, said in a statement. “A week before an election, Gov. Abbott and Attorney General Ken Paxton issued a partisan political attack that isn’t rooted in the needs of families.”Dr. Megan Mooney, a licensed psychologist in Houston, is also a plaintiff in the lawsuit. Dr. Mooney, who is required to report suspected child abuse under Texas law, has a practice that includes transgender patients, many of whom have been diagnosed with gender dysphoria, according to the suit.The moves by Mr. Abbott and Mr. Paxton, both two-term Republican incumbents, came days before a primary election in which each faces significant and noisy challenges from far-right opponents. Mr. Paxton, who has been indicted on securities fraud charges and accused of corruption by his own former top aides, has been seen as particularly vulnerable. Going into Tuesday’s primary, he appeared unlikely to receive more than 50 percent of the vote and was likely to end up in a May runoff.Paul Castillo, senior counsel at Lambda Legal, said in a statement that Mr. Abbott and Mr. Paxton were “joining a politically motivated misinformation campaign with no consideration of medical science and seem determined to criminalize parents seeking to care and provide for their kids,” adding that “gender-affirming care for the treatment of gender dysphoria is medically necessary care, full stop.”The officials’ moves had been praised, however, by some groups that oppose such treatments. “Minors are prohibited from purchasing paint, cigarettes, alcohol, or even getting a tattoo,” Jonathan Covey, policy director for the group Texas Values, said in statement last week. “We cannot allow minors or their parents to make life-altering decisions on body-mutilating procedures and irreversible hormonal treatments.”The effort to stop treatments for transgender teenagers has been sharply criticized by professional medical groups and by transgender health experts, who have said that such decisions, particularly those that carry medical risks, should be weighed by a patient, their parents and their doctors. Studies have found that transgender teenagers are at higher risk of suicide.The medical community has been debating when such treatment is appropriate, as an increasing number of teenagers have sought to better align their bodies with their gender identities through hormones and surgeries.At the same time, legislation to ban gender-affirming treatment for teenagers has been introduced in more than 20 states, including in Texas, though no such bills passed there during the last legislative session. In Texas, one of the bills would have redefined child abuse to include gender-affirming treatment for transgender children.After those bills failed, Mr. Abbott last summer directed the state’s protective services agency to determine whether surgeries for transgender teenagers would constitute child abuse. The agency also removed information about gender identity and about a suicide prevention hotline from its website after one of Mr. Abbott’s Republican primary opponents, Don Huffines, attacked the governor for “promoting transgender sexual policies to Texas youth.”Then late last month, Mr. Paxton issued his opinion, and Mr. Abbott responded with his directive. According to the filing on Tuesday, the agency began its investigations almost immediately after.