Because of the presence of a GCIU logo, this is likely not from the 1981 original release but a re-release from later in the 1983. This note from an emovieposter.com auction explains why:

Note that there are two versions of this poster: one with a GAU printer logo and one with GCIU logo. We have been told that the GCIU logo wasn’t trademarked until July 1983, so the theory is that any poster that carries the GCIU logo must be from 1983 or later and are either theatrical re-release posters or possibly video store posters. We do not know for sure.

A unique design and artwork on this English one sheet for the Eddie Murphy, Nick Nolte comedy action film 48 Hrs. In 2012 I met and interviewed the artist responsible, Brian Bysouth, and the resulting article can be read here. This poster was briefly discussed:

Another favourite of mine is your painting for 48 Hrs, which features Eddie Murphy raising his middle finger. Was that from your design?
No, I can’t recall who designed that. I need to check my invoice books to confirm, as I’d always write who briefed me to do the painting. Sorry, but I never really liked that design. I’d been given poor reference material and I think Nick Nolte’s likeness is fairly dire. I spent a while on it because of that difficulty but really didn’t like the painting because I never liked the design.