Police say they have had three reports in the last three weeks of windows being broken after being shot at on West Street between the junctions of Granville Road and Belvedere Road.
Scarborough Police said: "On each occasion, unknown offenders have targeted properties with possibly a BB gun or similar.
"Please remain vigilant, and report anything suspicious to 101 or anything ongoing to 999."
Information can also be passed on anonymously via Crimestoppers on 0800 555111.