Officers previously released images after an attempted burglary in Moor Grange Drive, West Park, in the early hours of April 6.
Now they are linking that incident to a burglary at a house in Spen Lane, West Park, earlier this month.
An Audi A4 was stolen during the burglary on May 6.
A spokesman said bank cards were also taken and later used at shops in the Bramley area.
Anyone who recognises the men or who has any information that could assist the investigation is asked to contact PC 3280 Adam Lawson on Leeds District Crime Team via 101, quoting crime reference 13180216414.
Information can also be passed on via the Contact Us section on the force website or by call the independent charity Crimestoppers anonymously on 0800 555 111.