Residents are seeking support for a 4.5-mile bike path that would connect with a 2-mile path in Mansfield. Adam Recchia, principal transportation planner for the Southeastern Regional Planning and Economic Development District, said Norton residents contacted the agency for help, and he set up an information session that drew more than 50 people March 12. He plans to forward a list of names to the Board of Selectmen so it can, if it chooses, appoint a committee. If the board were to approve, the town would apply for federal funding that would cover 80 percent of the cost, and state funding that would cover 10 percent. The cost of an off-road path ranges from $450,000 to $1 million per mile. Residents hope for a parallel equestrian path, as Mansfield has, he said. About a half-mile of the new section would be in Mansfield.