A hearing on the city's proposed budget is scheduled for Tuesday at 7 p.m. at City Hall. Council members should vote on the proposed budget on May 13.
If the department gets the extra officers, the overtime shouldn't be needed next summer, Jones said.
City officials support the overtime request, but the council still needs to approve the funding, said Mayor Steven T. Sager.
Next Tuesday, council members are expected to vote on whether to approve $12,960 for this fiscal year for the overtime, officials said.
They would consider another $12,960 to cover late summer overtime when they vote on the proposed budget on May 13.
The funds will come from community development block grants.
Under the overtime plan, two officers would work six hours of overtime four nights a week from May 1 to Aug. 31.
They would work in low- to moderate-income neighborhoods where there have been significant problems, Jones said.
The officers will address problems including noise violations, curfew violations, underage drinking and fighting, he said.
Neighborhoods the officers would patrol include George Street from Winter Street to High Street; Ross and Lanvale streets; East Antietam Street; downtown; and Walnut and Church streets.