Some batteries are considered hazardous waste and have to be taken to a Household Hazardous Waste Collection. You shouldn't have to pay yourself at the collection since Laconia is a participating town. The town gets billed based on how many residents participate in the collection. You can call the RPC and ask about your specific battery. If you don't get anywhere with it, PM me and I can put you in touch with someone in my office who specializes in hazardous waste collection in the western portion of NH.
http://lakesrpc.org/serviceshhw.asp