SJC Controller described a TCAS RA event when an Air Carrier on final for Runway 30R conflicted with a traffic watch aircraft on the Tower frequency; the reporter indicating the traffic watch aircraft should have been transferred to the Approach Control.

Narrative

Construction started on Taxiway W next to Runway 30L so we could only use Runway 30L for departures and all arrivals were landing on Runway 30R. This is a new procedure at SJC due to the taxiway construction which puts the aircraft on final north of course because they are on the VOR/DME Runway 30R. A traffic watch was southeast bound along Highway 101 at 2;500 FT on a morning traffic watch route and I pointed the aircraft out to Licke and worked him because they normally turn around at an 8 mile final and come back into SJC airspace. I called traffic on a B737 aircraft on a 3 mile final that the traffic watch observed and passed by about 2 miles. The B737 checked on at about a 12 mile final and I cleared him to land Runway 30R behind company on a 3 mile final. I had a helicopter hand off from NUQ that I RADAR identified and departed a Saratoga VFR to SCK off Runway 30L whose transponder was not turned on. I saw the conflict alert on a C172 and the B737 and called traffic to the C172 at about 1 mile opposite direction with B737 descending out of 2;800 FT. The Cessna had B737 in sight and I called traffic. The B737 said he had a TCAS RA and was climbing to 3;000 FT. The B737 again reported a TCAS RA on a 3 mile final. Recommendation; I would recommend handing off the traffic watch aircraft to Licke because of the close proximity of HWY101 to the VOR/DME approach to Runway 30R. I also recommend saying 'maintain visual separation' to the traffic watch after giving the traffic. A Supervisor said the NCT Supervisor was watching the conflict but no one from NCT called me to tell me about it. If someone sees the Conflict Alert at NCT they should call the SJC Tower Controller and advise them; like they do for low altitude alerts.