A property tax rate increase came a little closer to reality at Lawrence City Hall as commissioners did nothing to rebuff the idea at a Tuesday budget study session.

In fact, one more commissioner said strong consideration would have to be given to a rate hike, especially to address concerns he has about a shortage of police officers in the city.

“I think there is only so much time you can put off expenditures and reduce overhead, especially when you do have inflation to deal with,” said City Commissioner Mike Dever, who has lobbied against raising property taxes in the past. “At this point, it is hard to see how we’re going to find the revenue if we don’t raise taxes.”

Dever’s comments come one day after Mayor Aron Cromwell said he thought it would be difficult for the city to avoid a mill levy increase.

At Tuesday’s session, City Manager David Corliss essentially told commissioners that he plans to recommend a mill levy increase as part of his recommended budget, which will be released in early July.

“Raising the mill levy is never my first option,” Corliss told commissioners. “Cutting expenditures is what we look to do first, but I’m looking and not seeing anything significant that I can recommend.”

Commissioners didn’t give any indication of how large of a mill levy increase may be in store. A 1.7 mill increase is assumed to fund an expansion of the Lawrence Public Library, which previously was approved by voters. But Corliss has presented scenarios that have included a mill levy increase of more than four mills to fund additional police officers, employee wages and other city items.

Dever said he would be most likely to increase the mill levy in order to fund additional police officers. Those plans have called for anywhere from a 2.8 mill to a 3.6 mill increase to add from five to 14 additional police positions. Those mill levy totals also include the 1.7 mills for the library. A mill is $1 in taxes for every $1,000 in assessed valuation.

In other budget news, commissioners:

• Were presented a plan to use $1 million in infrastructure sales tax money to buy new radios for the city’s police, fire, public works and utilities departments. The new radios are required under federal regulations that require public agencies to switch to new frequencies by the end of 2012. The radios will cost about $2 million. The remaining million would come from a variety of city reserve funds. The infrastructure sales tax was approved by voters in 2008, with the idea that it would be used primarily for streets, but it also included a provision about improving public safety infrastructure, such as fire engines. The city has interpreted the ballot language to allow for the sales tax dollars to be used for the radios. Corliss said the unscheduled purchase won’t require other sales tax projects to be pushed back because the city had been conservative in estimating the revenue the sales tax would generate.

“We didn’t want to overpromise in the beginning,” Corliss said.

• Debated how much of a $7.6 million reserve fund the city should use to help fund the city’s health insurance program. Staff members told commissioners they were comfortable using $780,000 of the reserve fund for 2012 but had serious concerns about using more than that. The city runs its own health insurance program and relies on the reserve funds to cover unexpected expenses. The issue is being debated by commissioners because there is a proposal to raise the premium levels and deductibles on the city plan to make it more financially self-sustaining in future years.

Commissioners are expected to approve a 2012 budget in early August.