The main provision of the Constitution that can be violated by procedures used by the police to identify suspects is the guarantee of due process. The due process clauses of the 5th and 14th Amendments have been taken, in part, to mean that the government must deal fairly with suspects. This means that the police are not supposed to use identification procedures that unfairly push witnesses to identify a certain person.
The 6th Amendment can also be relevant. The state is supposed to provide suspects with a lawyer at all critical steps of a criminal prosecution. This can include times when police ask witnesses to identify a suspect.
These are the major constitutional provisions that can be violated by police identification procedures.