"Definitely dodgy," agreed George. "So he wouldn't even tell you who's supposed to be plotting all this stuff?"
- speaking of Dobby (CS3)
"Isn't that what he was doing the night he was supposed to be tailing me? Picking up dodgy cauldrons?"
- Harry on Mundungus (OP6)
Unreliable, with slightly criminal or less than honest overtones. Probably derived from “dodging the law”.