It is understood Mr Stafford, of Sandicroft Place, Preesall, was arrested by police on Friday and taken to Fleetwood police station where he was released on police bail pending further inquiries.
The part-time handyman and gardener had been an independent member of the towncouncil for several years, and had only recently been appointed Mayor for the second time.
He served in the post for the first time four years ago In a statement to The Courier, Preesall town clerk Mr Lionel Marr said he had received a phone call from Mr Stafford on Saturday. Mr Marr said: "He offered his resignation as Mayor and councillor. He sounded quite upset. I understand the matter is in the hands of the police. I have no idea what it is about."
Mr Stafford, a bachelor, has lived in the village all his life and is a well-known personality in the rural community.
Mr Marr's wife, Mrs Jill Marr, is the currentMayoress of Preesall and Knott End, and had previously agreed to accompany Coun Stafford on civic engagements.
Mr Marr said his wife would also now be standing down so that the current Deputy Mayor, Coun Rosina Lawson, who is likely to take over the mayorality for the rest of the civic year, would be free to choose her own Mayoress.
Preesall is one of only two parishes within rural Wyre district to have town council status, and along with it, the position
of Town Mayor. The other town council in rural Wyre is Garstang.
¦ IN a statement Lancashire police press office said: "A 58- year-old man has been arrested on suspicion of burglary in a dwelling. He has been released on police bail to report back to Fleetwood police station on July 23. He has not been charged."