Connecticut mayors grappling with rising retirement costs and sinking economies this week issued a distress signal to lawmakers in Hartford: Save us from our public unions.

The state would be in a “stronger position if we don’t negotiate for benefits,” Joe DeLong, the executive director of the Connecticut Conference of Municipalities, told a committee convened by the legislature to restore fiscal stability and economic growth. The conference of municipalities implored the state to end collective-bargaining for pensions and...