Reduce the following decision problem to CNF-SAT
Yes, you certainly can reduce it to SAT: the problem you state is obviously in NP, and thanks to Cook's theorem, everything in NP can be reduced to SAT.

I suspect that wasn't what you actually meant to ask.  Actually, your problem is in P: Hall's theorem says that such an assignment exists if and only if the corresponding bipartite graph has a perfect matching.  You can test whether a bipartite graph has a perfect matching in polynomial time using standard algorithms.