"Crime on Mars" aka "Trouble With Time", a short story by Sir Arthur C. Clarke.
It matches with the head and the non-humanoid aliens:
Although I'd never seen the original, like most other departing tourists I had a replica in my baggage. It bore the certificate of the Mars Bureau of Antiquities, guaranteeing that "this full-scale reproduction is an exact copy of the so-called Siren Goddess, discovered in the Mars Sirenium by the Third Expedition, A.D. 2012 (A.M. 23)."
It's quite a tiny thing to have caused so much controversy. Only eight or nine inches high—you wouldn't look at it twice if you saw it in a museum on Earth. The head of a young woman, with slightly oriental features, elongated earlobes, hair curled in tight ringlets close to the scalp, lips half parted in an expression of pleasure or surprise—and that's all.
But it's an enigma so baffling that it has inspired a hundred religious sects, and driven quite a few archeologists out of their minds. For a perfectly human head has no right whatsoever to be found on Mars, whose only intelligent inhabitants were crustaceans—"educated lobsters," as the newspapers are fond of calling them. The aboriginal Martians never came near to achieving space-flight, and in any event their civilization died before men existed on Earth.
No wonder the Goddess is the Solar System's Number One mystery. I don't suppose we'll find the answer in my lifetime—if we ever do.