all primes (except 2--but 3 is obviously not a perfect square) are odd. That means the perfect square must be even. And as EP has said 4 is one of them and I also don't know if there are any other options.
Brute Force. I tried all of them from 12 to 1002 inclusive. 4 is the only one I found. Actually, I didn't try all of them. It isn't necessary to try numbers whose square ends in a 1, 5, 6, or 9.