The homeowner took a picture of the man, who was wearing sunglasses and a construction hat.
It happened on Willow Drive on September 1 around 8 a.m.
The homeowner called police, but the man got up and left before officers arrived.
Suffolk County Crime Stoppers is offering a cash reward of up to $5,000 for information that leads to an arrest.
Anyone with information on this incident can contact Suffolk County Crime Stoppers to submit an anonymous tip by calling 1-800-220-TIPS, texting "SCPD" and your message to "CRIMES" (274637).
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