Look at the owner's manual for your compressor if you have it. The manual will say that it is made by Campbell Hausfeld. Look through the information on the cover or at the beginning of the manual to see if it says it is made by this manufacturer.
Determine what color the air compressor is. Campbell Hausfeld air compressors are known for their signature deep blue color. If your air compressor is any other color, then it is not a Campbell Hausfeld.
Look at the motor housing. Campbell Hausfeld air compressors all have a "CH" logo on the housing.