City Hall officials are running out of time to redraw Boston’s City Council district precinct lines and could potentially miss out tens of thousands of dollars, if not millions, in cost savings, a top voting expert says.

The number of residents in precincts across the city varies widely, leading to an uneven distribution of Election Department resources on election days and a waste of money while the city struggles with a budget that features declines in state aid and rising health care costs for municipal employees, supporters of overhauling the precinct lines say.

For example, one precinct may have thousands of voters, as is the case in Chinatown, leading to long lines on Election Day, while another precinct may have just a few, such as the Harbor Islands.

Cities and towns are required by state law to equalize the precincts every ten years, after the federal census is completed, but Boston is exempt. The city last undertook re-precincting, as the process is called, well over 70 years ago.

“Time is of the essence,” said Cheryl Crawford, policy director for the local voting rights group, MassVote.

City officials must act on re-precincting by June 15, the same day the rest of the state’s cities and towns are expected to complete their process, she said. Otherwise, she added, Boston will have to wait until the next U.S. Census rolls around in 2020.

The City Council should pass a home rule petition lifting the exemption by May 15, allowing for the process to get underway, Crawford said.

Others are more cautious about the process, describing re-precincting as a complex task, particularly when some neighborhoods identify with their precincts, and may be unwilling to change.

The city’s election commissioner, Geraldine Cuddyer, could not be reached for comment, although the city’s legal department is reviewing the matter.

State Rep. Michael Moran, a Brighton Democrat overseeing the separate redrawing of state House, Senate, and Congressional districts, known as redistricting, set the June 15 deadline for cities and towns to finish re-precincting. When asked whether he supports the same for Boston, he noted Boston’s exemption. “That’s something they’re going to have to decide,” Moran said. “If they want to do it, they can.”

State Sen. Sonia Chang-Diaz, a Jamaica Plain Democrat who is serving on the legislative panel on redistricting with Moran, said she supports re-precincting efforts.

Lawrence DiCara, a former city councillor who specializes in redrawing political lines, has said that with the right equipment and information, he can do it in one weekend if the city and the secretary of state’s office agree on how to get re-precincting done. “We may be out of time for this cycle,” he told the Reporter this week. “But it is a doable activity if the city and the state agree upon it.”

District 8 City Councillor Michael Ross, who represents the Back Bay and Mission Hill, is the sponsor of the home rule petition lifting the exemption, and said it would be “unacceptable and irresponsible” for the city to wait ten years before attempting to re-precinct. “We’re the only city in Massachusetts that has this exemption,” he said. “It’s something every other city is able to do every ten years.”