HARTFORD — There’s no better way to understand how the state’s fiscal woes will affect municipal budgets than to hear from the people in charge of them, Rep. John Rigby said Tuesday. More than two dozen leaders-mayors and first selectmen-from communities throughout the state were at the Capitol for a roundtable discussion organized by House Republicans. Municipal leaders such as Goshen First Selectman Robert Valentine and Torrington Mayor Ryan Bingham gave legislators suggestions about how they could make life easier for their communities in the face of a massive state budget crunch. Rolling back unfunded mandates and temporarily suspending binding arbitration were among the suggestions from the invited group, which also included Kent First Selectman Ruth Epstein. Local leaders called for even greater communication as the budget crisis continues to unfold. “Municipalities are further ahead in building their budgets than the state is, and that poses a big problem for officials at the local level who are worried about how to balance their books in these tough economic times without significant tax increases for residents,” Rigby said Tuesday afternoon. The roundtable session with local officials started with a status report on the state budget from a representative from the nonpartisan Office of Fiscal Analysis. The presentation was well-received by the local officials, split evenly as representatives from both sides of the aisle. Most called Tuesday’s nonpartisan approach refreshing. At present, Gov. M. Jodi Rell has forecasted a budget deficit of more than $900 million for this fiscal year. The numbers are even worse for coming years-in the billions, perhaps. For the local officials Tuesday, financial aid from the state was a concern-particularly funding for education. Most municipal leaders said they would be happy to at least receive the same amount of money as last year. At the end of the two-hour session, the invited guests told House Republican Leader Larry Cafero, of Norwalk, that they look forward to meeting again as the legislative session proceeds. “For state legislators, these types of events are a great way to not only give the people you work for a clear understanding of what’s going on with the budget, but also for them to tell us what specific actions we can take to help them as they try to run their towns,” Rigby said. “I can’t wait for the next one,” he said.