The future of Roe v. Wade may be in doubt, but reproductive rights groups and their allies are divided about asking voters to add abortion rights to Connecticut's state Constitution.

On Tuesday, Gov. Ned Lamont held a ceremonial signing for the nation's strongest abortion law. The Reproductive Freedom Defense Act makes Connecticut a "safe haven" for abortion providers and patients. Courts are now banned from helping other states sue clinics -- including handing over medical records. Also, the governor cannot extradite people who are prosecuted for abortion in states like Texas.

"This law says to people all over the country essentially, 'Texas, don't mess with Connecticut,'" said state Rep. Matt Blumenthal (D-Stamford), co-chair of the legislature's new Reproductive Rights Caucus.

The new law also expands access to abortion, especially in rural areas. Physician assistants, advanced nurses and midwives can now perform first trimester procedures.

But minutes after signing the law, Lamont said Connecticut could go even further.

"It doesn't bother me having a constitutional amendment," he said. "If it takes a little more time, let's make that something that can't be jiggered with in future administrations."

But the idea is controversial, even among some advocates.

Abortion is already legal under state law. Connecticut was the first state to codify the Roe decision back in 1990.

This year, state lawmakers failed to vote on a proposed constitutional amendment. At a public hearing in March, critics said the language was so broad, it could strike down Connecticut's current ban on most third trimester abortions.

"What this amendment would do is, it would legalize abortion all the way up to just the moment prior to birth," said Peter Wolfgang, president of the anti-abortion Family Institute of Connecticut. "Most people are not on board with that."

Even supporters admit an amendment is risky because ultimately voters would decide.

"Referendums are tricky. You don't know turnout -- when are you going to do it? And again, what the question says can sometimes be very confusing," said House Speaker Matt Ritter (D-Hartford). "We tried to do early voting in 2014, and it got pummeled, right? Like a 16 versus one seed, OK? Because the question was too complicated."

But with abortion challenges mounting, others say not acting is even riskier.

"We are only an election away from losing [abortion rights] , so it's very important for people to think about that," said state Senate Majority Leader Bob Duff (D-Norwalk).

Even some Republicans are open to the conversation.

"I think it's going to be a conversation possibly for next session, depending on what that opinion looks like," said Rep. Vin Candelora (R-North Branford), the state House minority leader.

No matter what happens, voters aren't likely to decide anytime soon. Unless lawmakers call a special session this summer, the earliest an amendment could hit the ballot would be November of 2024 – and more likely the year 2026.

So far, no other state has added reproductive rights to its state constitution. But voters in Vermont will decide this fall, and New York and California are considering it.