Of questionable legality, like a scam, or questionable moral or structural integrity. Originally British.
"Ehhh, I dunno, that piece is pretty dodgy. It's all rusty, hasn't been used in a few decades, it might fall apart."
"Smuggling ganja out of Mendocino could get some tall dollars, but it's a dodgy scam, the cops proly bust people for that all the time."