Perfect hash function Is a perfect hash function always bijective ?
  In Wiki  "In mathematical terms, it is a total injective function" but it does not mean, that it is bijective.
No, it is not always bijective.

A perfect hash guarantees that no two inputs (from the set of valid inputs) collides, so it is clearly a 1 to 1 mapping.  However, in the case where the output range contains more possible values than there were valid inputs, there will be outputs which do not map back to inputs.  hence it is not bijective.

If you restrain the problem dramatically, and define the range of the outputs to be "the set of outputs attained from valid inputs," then you could argue it is bijective because you have constrained the output sufficiently to make such a claim.  However, it would be up to you to explain why this very particular output range is a valid one for whatever topic is being discussed at that time.