The force say the incidents happened on two occasions on December 15 at about 3.22am and at about 2.55am the following day.
Both incidents took place in Hardenshaw Lane, Camblesforth.
A police spokesman said: “Unknown individuals attempted to gain entry to a property and stole two bicycles from outside.
“If you recognise the man in the CCTV image, please contact us, as he may have vital information to assist our investigation.
“You can email freya.smith@northyorkshire.police.uk or call North Yorkshire Police on 101, select option 2, and ask for Freya Smith.
“Alternatively, you can contact Crimestoppers anonymously on 0800 555 111 or via their website.”
Please quote reference 12240229157 when providing any information.
