"I Dream of Cheezy" is a play on this 1965 TV series, and the mouse genie Cheezy is based on the title character of said TV series, but is instead a male.
In the episode "I Dream of Cheezy", the logo on the sign for Sgt. Boffo's Ferocious Feline Mouse-Bashing School features an emblem of a mouse slashed out, similar to the Ghostbusters logo from its movie and franchise of the same name.