I am not sure where you are located however, in Canada there is a section in the Criminal Code (s.494) that allows any citizen to arrest without warrant, any person they FIND COMMITTING an indictable offence. For purposes of arrest a Hybrid or Duel offence is considered indictable. I believe the US has a similar citizen's arrest law.
Regardless of being a P.I. or not the investigator is still a citizen and this would apply to him or her.