Small Aircraft; Low Wing; 1 Eng; Fixed Gear
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 2
Confusion; Communication Breakdown; Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Clearance
Flight Crew Returned To Clearance
Human Factors; Procedure
Aircraft X called in bound from the south (reported circling over 680/24 interchange); I didn't catch his call sign so I told him to enter and report a 2 mile left base for runway 32L; and say again his numbers.  On his read back he gave his call sign again; but cut out before the assigned runway so I had him verify a left base for 32L and he verified left base for 32L.  Upon review of the tapes I realized that while he verified a left base for 32L he did not verify the 2 mile report.  At this time I also had 2 aircraft in right closed traffic for 32R; another departing 32R North bound and a aircraft entering the 45 for 32R to join the pattern (this aircraft also being traffic for the departing aircraft). I had a aircraft in left closed traffic for 32L as well.  Aircraft X reported that he had a NMAC with Aircraft Y that he overflew he reported at 30 ft.  I asked him to say position and altitude he reported altitude of 800 feet about to turn left base for 32L.  I then saw that he was not 'about to turn base' rather he was already on a short approach to overfly the tower on a left base for 32L; I told him that I had not heard his 2 mile base report and told him to go around and continue in left closed traffic.  Aircraft Y never reported a NMAC or anything else.   Aircraft X went around and landed with no further incident. The weather at the time was hazy; I was spotting aircraft out the window about 3-4nm out.  When asked one of the pattern aircraft reported in flight visibility at 6-7nm.I had a lot happening on 32R and my attention was focused on giving traffic to my departing aircraft and incoming aircraft as well as sequencing the other aircraft in their pattern sequence.  I never got a position report on Aircraft X until it was too late; neither did I see him on the radar; but I should have paid more attention to the other runway.  I only had the one aircraft in the pattern for 32L; but I knew Aircraft X was inbound; I should have been thinking that it had been awhile since he called inbound where is he?  I should also have made sure he read back the need for a 2 mile base report.
CCR Tower Controller reports of a reported NMAC by an aircraft that did not report a 2 mile left base.