Officers said that at about 1.50am on Friday, June 30, a man and a woman climbed over a wall to gain access to Knaresborough Bowling Club on Park Parade.
A North Yorkshire Police spokesperson said: "Whilst in the grounds of the bowling green the man kicked open a secure door and broke the lock.
"Officers would like to speak to the man pictured on CCTV, as he may have important information that could assist the investigation."
Anyone who recognises the man pictured is asked to call 101, select option two and ask for Pierre Olesqui or email [email protected]
Alternatively, call Crimestoppers anonymously on 0800 555 111.
Quote reference number 12170116855 when passing on information.