Should Richmond’s top priority be modernizing obsolete public school buildings or replacing the 47-year-old Richmond Coliseum?

Veteran political strategist Paul Goldman wants to give city voters the opportunity to weigh in on that issue.

He said on Tuesday that he has decided to submit paperwork to the Richmond Circuit Court seeking approval to circulate petitions for a ballot initiative that would limit the amount of tax dollars that could be used to pay for a new Coliseum.

The proposal would not directly challenge the no-money-down plan that a group led by Dominion Energy Chief Executive Officer Thomas F. “Tom” Farrell II is advancing with the support Mayor Levar M. Stoney.

Still under wraps, but expected to be unveiled shortly, the plan generally calls for tearing down the old Coliseum, building a larger replacement arena and using all of the tax dollars generated from developments to be built in a 10-block area around the new arena to repay the proposed arena’s $220 million cost over 30 years.

The other developments, projected to generate more than $1 billion in property value if private investors undertake them, are to include 2,800 apartments, an upscale convention hotel, at least four office buildings and an array of retail stores and restaurants, according to the Farrell group, known as NH District Corp.

Mr. Goldman’s ballot initiative would allow only 51 percent of the tax dollars generated in the special district to be used to repay the cost of building a new 17,500-seat arena. The rest of the new tax money, 49 percent, would be required to be spent to modernize Richmond’s public school buildings.

Mr. Goldman laid out the arduous process that he and the allies would face in pushing an initiative that would both allow redevelopment in Downtown and generate a new stream of revenue for school construction.

If the court approves the ballot language, Mr. Goldman said he and others would have nine months to collect the signatures of nearly 14,000 registered voters on petitions to put the proposed charter change on the ballot.

The number of signatures represents about 10 percent of city voters who cast ballots in the 2016 presidential election.

Once that is accomplished, the court would need to set a date to hold a vote or referendum on the initiative, possibly in a special election. If the initiative wins voter approval, it would then need to pass the General Assembly and have the governor’s signature to go into effect.

Mr. Goldman, who played key campaign roles in helping L. Douglas Wilder become the first African-American to win statewide election for lieutenant governor and for governor in the 1980s, has been through the initiative process twice before.

In 2003, he led the effort to allow voters citywide to elect the mayor rather than leaving it to City Council.

In 2017, Mr. Goldman successfully pushed a charter change requiring the mayor to provide a fully funded plan to renovate or replace the city’s worn-out school buildings without raising taxes or explain why he could not.

Mayor Stoney has until January to comply.

Of the city’s 44 public schools, only eight were built in the past 20 years, including the four built during the tenure of Mayor Dwight C. Jones, Mayor Stoney’s predecessor.