Termination of translation
Shigeta's got a point: the ribosome is latched onto the mRNA so those two are intrinsically linked.  You're really asking whether the ribosome comes off first or whether the tRNA does, but it's actually the new polypeptide, which makes sense:


  The stop codon is recognized by a protein, the polypeptide chain release factor (RF), which triggers the hydrolytic release of the nascent polypeptide chain from the P-site-bound peptidyl-tRNA.


This minireview puts forth a model (see below) where, in E. coli at least, the 50S ribosome subunit is then dissociated from the mRNA/30S subunit/tRNA complex, following which the final tRNA is removed.  An in-depth review from a few years later gives more context.