Glass was smashed after ball bearings were shot at property in the Castle Woods area of Redlynch.
The first of two incidents near Vale Road took place at approximately 6pm on Monday, September 11 and the second took place at approximately 5pm on Thursday, October 19.
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Police are uncertain how the bearings were fired, but it is believed to have been either a catapult or air-related weapon.
Wiltshire Police is now appealing to the public for witnesses and dash cam footage.
Anyone with information, or who saw anybody carrying an item capable of firing projectiles, has been asked to call the police on 101, quoting reference number 54230111647.
Wiltshire Police reiterated that a Public Space Protection Order remains in place in Downton and Redlynch which prohibits anyone from carrying a catapult on their person at any time.
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