ALBANY — Vincent Leibell, who is facing a federal investigation over the purchase of his home, has resigned as a state senator and announced he’s stepping down as Putnam County executive — a post to which he was elected just last month.

In a one-sentence letter released yesterday, the 64-year-old Republican wrote that he had left the state Legislature as of 11:59 p.m. Thursday. His Senate term would have expired on Dec. 31.

Putnam County officials are trying to figure out how to determine who’ll be county exec on Jan. 1.