A perfect hash function will result in $\cal{O}(1)$ worst case lookup.
Moreover, if the maximum number of collisions possible is $\cal{O}(1)$, then hash table lookup can be said to be $\cal{O}(1)$ in the worst case. If the expected number of collisions is $\cal{O}(1)$, then the hash table lookup can be said to be $\cal{O}(1)$ in the average case.
