With Connecticut’s state budget in limbo, many cities and towns have blindly set their local tax rates for the new fiscal year beginning July 1, hoping they won’t need to send out refunds or supplemental property tax bills to cover any gaps in anticipated state aid.

The General Assembly adjourned June 7 without passing a new state budget that covers a projected two-year, $5 billion deficit. The state’s budget is typically about $20 billion a year. While lawmakers have said they hope to pass a new tax-and-spending plan before the fiscal year ends on June 30, it’s questionable whether that will happen.

Gov. Dannel P. Malloy met Tuesday with legislative leaders on the budget for the first time since the regular session adjourned. He said his administration is preparing for the possibility he’ll have to issue stop-gap budgets after July 1. Malloy plans to release “principles” next week that will guide how he expects to fund state operations on an interim basis.

While there have been several times when lawmakers did not pass a state budget before the new fiscal year, Betsy Gara, executive director of the Connecticut Council of Small Towns, said that this year is different because so much is up in the air.

“In the past, we had early indications of what municipal aid levels would be,” she said in a statement. “This is the first time there have been large fluctuations in the different proposals and how they may impact municipalities.”

Many cities and towns are anxiously waiting to see how the state plans to revamp its main education grant for public education, parts of which have been ruled as unconstitutional. Early proposals showed lawmakers might shift funds from small communities to larger ones. There are also concerns about whether a final budget agreement might include Malloy’s controversial proposal requiring municipalities to pay a share of teacher pension costs. Gara said many communities chose to craft local budgets that don’t account for the pension costs, in hopes the new expense won’t be part of a final state budget deal.

Kevin Maloney, spokesman for the Connecticut Conference of Municipalities, said city and town leaders will also need the General Assembly to pass legislation that will allow them to override local charters and send out supplemental bills, if required.