Once you have filed a missing persons report the police will entered the name into the national database and the police department will determine what category it will fit, for example if the person is a threat to himself or others.
Most police agencies will not actively search for an individual unless there are circumstances that warrant it, such as a child under 14, a senior with Alzheimer's, someone who is mentally handicapped, a mental health emergency, or if there is evidence of foul play, to name the most common. Because it is not against the law to "go missing," even though you are 100 percent sure that they did not disappear of their own free will, the police will only follow their protocol.
If the police do happen to come across the missing person, unless it falls under the above criteria, they will only ask them questions. You will receive a courtesy call. Most police agencies will tell you where they found the person, but they will not detain them. Some police agencies will send them on their way and later will let you know they ran across them, as long as the MP was obeying the law, doesn't have a warrant, is not suffering from a mental health emergency or is not intoxicated.
If you are searching for a loved-one and it has recently happened, to draw attention to your search, you should go to the media. If the media does not show any interest (this can happen if your missing person does not have a "hook" to their story) then contact me, and I will tell your story.
Also, considered a Private Investigator. Read my article on Why you should hire a private investigator to find out more.