The Milngavie man, who asked not to be named for fear that he may be targeted in future, alleges that a man was seen systematically going through gardens and driveways, often returning to the same gardens.
Residents called the police on the non-emergency 101 phone line.
He said: “Astonishingly within two minutes two police cross terrain motorcycles were on the scene. These bikes were versatile and were able to cover rough ground fast.
“One of the police riders guarded a main route, interviewed concerned homeowners then chapped doors and advised people to lock their cars.
“The other police officer rode round the area searching for the man but unfortunately he escaped through the backs of gardens and then was spotted in another area.
“One of the riders then sped off to search for him. Homeowners will feel reassured of this fast and thorough police response.”