SBA TRACON CTLR VOICED CONCERN REGARDING TWR ACTIONS; WHEN TRACON MISSED APCH INSTRUCTIONS WERE COUNTERED BY TWR'S ATTEMPT TO ISSUE A VISUAL APCH.

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I ISSUED THE APCH CLRNC AND SHIPPED THE ACFT TO TWR. THE TWR CIC WHO WAS BEING TRAINED CALLED TO ADVISE THE ACFT WAS EXECUTING A MISSED APCH AND THAT TWR WOULD BE KEEPING THE ACFT. I ASKED WHY AND DID NOT GET AN ADEQUATE ANSWER (EG; HE'S ON THE VISUAL). SO; I ISSUED ALTERNATE MISSED APCH INSTRUCTIONS 'FLY RWY HDG; MAINTAIN 3000 FT.' THE CIC TRAINER ASSERTED HIS AUTH. SUBSEQUENTLY; I OBSERVED THE ACFT FLYING IN A 4000 FT MVA AT 3000 FT (MODE C). I ISSUED A LOW-ALT ALERT TO TWR (LCL CTL). I SUBSEQUENTLY LISTENED TO ALL THE TAPES AND LEARNED THE ACFT CALLED MISSED APCH; RPTING 'WE NEVER SAW ANYTHING.' THE LCL CTLR ASKED THE PLT IF HE COULD BRING HIM AROUND FOR RWY 7. THE PLT SAID ALRIGHT. THE LCL CTLR ISSUED A VISUAL APCH WITHOUT ASKING THE PLT IF THEY HAD THE FIELD IN SIGHT. SUBSEQUENTLY; THE PLT REPEATED 'WE NEVER SAW ANYTHING' AND 'WE DO NOT HAVE THE FIELD IN SIGHT.' THE CTLR ACKNOWLEDGED THIS BUT DID NOT ISSUE A SAFE ALT AND HDG. TRAINING ON CIC WAS A FACTOR; AS THEY COORDINATED BADLY.