The bruglaries happened at 11.25pm on 14 March and 1.10am on 19 March, in the Bachelor Gardens area of Bilton.
The incidents involved a male suspect attempting to enter a property on two separate occasions by trying the door handle.
Police are particularly appealing for information about the suspect, described as white, male, and dressed in dark clothing, including a dark jacket with a hood and a small logo on the left breast. He was wearing gloves and a balaclava.
Please email ben.leslie@northyorkshire.police.uk if you have any information that could help our investigation, and if you live in the area surrounding Bachelor Gardens, please check any CCTV. Alternatively, you can call North Yorkshire Police on 101 and ask for PC285, or contact Crimestoppers anonymously on 0800 555 111 or via their website. Please quote reference 12250046377 when passing on information.