The home on Trafalgar Terrace was targeted during the early hours of the morning between July 21 and 22.
North Yorkshire Police said CCTV investigations are ongoing.
Witnesses who saw or heard the window being broken, or may have dash-cam footage from the area are urged to contact North Yorkshire Police.
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It follows a similar incident in Eastfield where a house window was smashed at the weekend; there is no suggestion the incidents are linked.
Anyone with information should email [email protected] or call 101, selecting option 2 and dial 30696.
Information can be passed on anonymously to Crimestoppers on 0800 555 111. Quote police reference number 12220128075 when providing information.