Mo. Rev. Stat. § 544.218: Arrest without warrant, lawful, when.

An arrest without a warrant by a law enforcement officer, including a uniformed member of the state highway patrol, for a violation of section 577.010 or 577.012 is lawful whenever the arresting officer has reasonable grounds to believe that the person to be arrested has violated the section, whether or not the violation occurred in the presence of the arresting officer.