AN A319 EXPERIENCED AN ELECTRICAL FAULT DURING ENG START AFTER TOW CREW DISCONNECTED. THE TOW CREW WAS REQUESTED FOR A GATE RETURN. CAPT RELEASED PARKING BRAKE BEFORE TUG CONNECTED STRIKING TUG AND DAMAGING ACFT.

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PUSHED BACK FROM GATE. STARTED #2 ENG DURING PUSHBACK. AT COMPLETION OF PUSHBACK; GND CREW TOLD US TO SET BRAKES; WHICH I DID. I RESPONDED WITH 'BRAKES SET; PRESSURE NORMAL; CLRED TO DISCONNECT.' DURING OUR START OF #1 ENG; RECEIVED ECAM MESSAGE '#1 IDG OIL PRESSURE LOW' AND '#2 GENERATOR FAULT.' I ABORTED #1 ENG START. CONSULTED WITH FO AND DECIDED TO RETURN TO GATE. WE BOTH MOTIONED VISUALLY FOR PUSHBACK CREW TO RECONNECT TO ACFT SINCE THEY WERE NO LONGER IN COM WITH US. THE GND CREW RECONNECTED INTERPHONE AND WE TOLD THEM WE NEEDED TO RETURN TO GATE FOR MAINT. I THEN HEARD TOWBAR BEING RECONNECTED; SO I RELEASED BRAKES; FORGETTING #2 ENG WAS RUNNING. ACFT ROLLED INTO TUG; STRIKING TUG ROLL BAR AND CAUSING DAMAGE TO #2 TOTAL AIR TEMP PROBE AND R LOWER NOSE OF ACFT. WE WERE TOWED BACK TO GATE. MADE PA TO PAX AND ACCOMPLISHED PARKING CHK. MOMENTARILY WAS DISTR BY ELECTRICAL PROB WITH THE ENG RUNNING. NON ROUTINE PROC OF HAVING TUG RECONNECT TO ACFT. NO COMPANY PROC FOR THIS. MIGHT HAVE BEEN BETTER TO LEAVE PUSHBACK CREW CONNECTED TO ACFT UNTIL BOTH ENGS STARTED IN CASE WE NEEDED TO CONTACT THEM WITH A PROB.