PRIVATE EYE: The American Sign Language (ASL) sign for "private eye / P.I. / private investigator"
May also be referred to as an investigator, detective or sleuth.

The term "private eye" or a "P.I. (private investigator)" is a 'slang' term in English that means 'a private detective' as opposed to one who works for the police or another authority.

One way you could convey the concept of private eye in ASL is by signing investigate with 'sneaky' facial expressions:

If you wanted to convey the concept of 'investigate' the ASL sign is:

Notes: 

See: DETECTIVE

See: INVESTIGATE