With little debate, the House of Representatives voted 126 to 18 Thursday night for legislation easing the way for transgender people to legally change their sex on birth certificates, drivers’ licenses and other forms of identification in Connecticut.

The bill allows a transgender person to legally change their gender before sexual assignment surgery, but after undergoing hormonal therapy and making the social and psychological transition to a new sex.

“It affects a very small group of people, but it makes a huge difference in their lives,” said Betty Gallo, a long-time lobbyist on lesbian, gay, bisexual and transgender issues.

On a practical basis, it means that a transgender person living as a woman no longer would have a drivers license or birth certificate that says she is a man.

“You can imagine the stigma coming with that,” said Rep. Matthew Ritter, D-Hartford, explaining the bill to the House.

Ritter said some transgender people are unable for medical reasons to surgically complete gender reassignment.

A new birth certificate, the document necessary for other forms of ID, could be obtained only with a medical affidavit stating the applicant had undergone surgical, hormonal or other treatment for gender reassignment.

Under current law, the gender on a birth certificate cannot be changed without surgical reassignment.

During a public hearing in March, legislators were told by the Human Rights Campaign that only one in five transgender people nationally have been able to update all their identification documents and records, including birth certificates, to reflect their appropriate name and gender.

“Transgender people with incongruent identity documents frequently experience violence and discrimination,” said Alison Gill of the Human Rights Campaign.

No one spoke in opposition Thursday during the House debate. The bill passed with the support of every Democrat and 45 of the 63 Republicans present.

To Gallo, the uneventful approval of a transgender bill was a political milestone, coming four years after the difficult passage of a transgender rights law without a single Republican vote.

“I think there’s been a new understanding of transgender people,” Gallo said.

The bill now goes to the Senate.