AMHERST — More than 20 years after first taking up the issue, Amherst Town Meeting is again endorsing legislation that would allow legal, permanent noncitizens who live in Amherst to vote in local elections on local matters, such as municipal budgets and candidates for town office.

But state Rep. Solomon Goldstein-Rose, D-Amherst, said May 18 that despite overwhelming support — with just four members voting against the measure — the concept may continue to be a non-starter in the state’s House of Representatives.

Already, Rep. Byron Rushing, D-Boston, has filed a bill called “An Act enabling cities and towns to extend voting rights in municipal elections to certain noncitizens of the commonwealth.”

Rushing’s bill would allow noncitizens who intend to become American citizens the right to vote in local elections.

“It requires approval from the Legislature, and Amherst, and other towns, have submitted this for approval following Town Meeting votes many times in past years with no success,” Goldstein-Rose said. “So I’m assuming some members or leadership in the Legislature do not agree with this policy and therefore likely neither of these options will move forward this year.”

If Rushing’s bill is passed by the Legislature, though, it would require adoption in each town both by Town Meeting and a majority popular vote at a municipal election.

Amherst has repeatedly agreed to appeal to the Legislature to allow so-called “legal aliens,” including graduate students at the University of Massachusetts whose children attend public schools, to vote on local issues in local elections. The measure passed, 153-4.

Support for the concept, originally brought to Town Meeting by Vladimir Morales in 1996, has been growing.

That year, the measure passed 96-41, but by 2009 it was OK’d 136-14 and in 2013 it passed 159-4. But it has always languished in the Legislature.

Matthew Charity, a Precinct 2 member and chairman of the town’s Human Rights Commission, said neighbors who pay taxes, send children to schools and volunteer in the community deserve to have more voice in town affairs.

Patricia Church of Precinct 5 also supported the measure.

“This is just the right thing to do. When people are living in our town — and raising their families in our town — and can’t decide who is serving on the School Committee, it’s just not right,” Church said.