The woman is believed to have stolen more than £1,000 worth of scratch cards from shops across North Yorkshire and also from retailers in West Yorkshire and Greater Manchester.
She manages to distract shop staff and takes the cards when they are not looking.
The woman officers would like to speak to in connection with the thefts is described as white, aged in her late 20s to early 30s, with a medium build and blonde hair, usually tied up in a bun or pony tail.
Anyone who can help identify the woman is asked to contact North Yorkshire Police on 101, select option 2 and ask for PC David Furlong.
If you prefer to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Please quote incident number 12130109193 when passing on information about this appeal.