No, Many shows have publicized the 24 or 48 hour waiting period to report missing people but that doesn't exist in real police departments. As soon as you know a child or adult is missing, report it to police. 

It is not against the law for an adult to go missing, so in some cases the police will not actively investigate without proof of foul play.  You should still file a police report asap and take note of the police report number. 

Go into the police station in person to file the report.  You can insist and request to speak with a supervisor. Look on their website, many times it states their criteria to report a missing person.

If the police refuse to take a missing person report, ask them specifically why they are refusing.

You can reach out to media for coverage or an attorney to help persuade the police to open a missing person report. 

According to the National Criminal Justice Reference Service, "To date, there is no official definition for a “missing person.” Examination of federal, state, and local laws provides a general understanding of a missing person to be an individual who, voluntarily or involuntarily, cannot be located because their whereabouts are unknown. The lack of a uniform definition stems from very little standardization nationally across policies, protocols, and practices governing how missing person cases are handled. "