Do you need to investigate a missing person?
Yes, law enforcement is required to investigate a missing person after they are found. This is because that person may have been kidnapped, but they haven't found the kidnapper yet, so they could have information on where the kidnapper may be. Also, sometimes the missing person in question may have just ran away, causing a lot of people to go out there way, and spend a lot of money to find that person.
It could be a good idea to use resources on your own before or after the police do their investigation but not during. It could conflict and confuse those questioned and make it more difficult for police.