Not an answerable question, in my opinion.
In order to determine the legality of signatures on petition, you would first have to determine what that particular petition requires for the signatures.
A petition warrant article in Alton requires "x" number of Alton Residents to sign the petition.
I have signed petitions that required the signature of a resident of NH.
There may be no legal residency requirements for a petition.
You need to determine what the legal requirements are for the petition and then get signatures in accordance with those requirements.
From my end, renting a slip, valet, even season resident may not qualify for a petition.
Maybe we need a lawyer to chime in: check out callawinnilawyer.comm.