CL601 FLT CREW EXPERIENCED CONFLICT WHILE LNDG AT HOU AS HELI PARALLELING RWY OVERFLEW ACFT.

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WE WERE FLYING A VISUAL APCH TO RWY 4 AT HOU; WHEN AT APPROX 200 FT WE NOTICED A HELI; AT OUR ALT; OFF OUR R SIDE LOCATED ABOUT THE AREA JUST S OF TXWY J AND TXWY K FLYING PARALLEL TO RWY 12R/30L IN A NW DIRECTION. THIS WOULD PUT THE HELI DIRECTLY OVER OUR RWY; JUST BEYOND OUR TOUCHDOWN POINT; AT THE EXACT TIME WE WOULD BE LNDG. THERE WAS NO CALL FROM THE TWR TO US IN REGARDS TO THIS HELI TFC; AND WE WERE AT A POINT WHERE WE WERE COMMITTED TO LAND. WE WERE NOT ABLE TO CONTACT THE TWR AS THE FREQ WAS TOO CONGESTED. OUR ONLY CHOICE WOULD HAVE BEEN TO GO AROUND AND PROBABLY OCCUPY THE SAME AIRSPACE AS THE HELI; OR CONTINUE THE LNDG AND RISK HAVING TO COMMIT TO LNDG AS THE HELI FLEW ABOVE US; NOT ALLOWING US TO PERFORM A LOW ALT GAR IF ANYTHING WENT WRONG WITH OUR LNDG. AFTER LNDG AND JUST TURNING OFF THE RWY; I QUERIED THE TWR AS TO WHY THE HELI WAS OVER OUR LNDG RWY WITH NO TFC CALL. THEY DID NOT ANSWER. WE QUERIED THEM AGAIN; STILL NO ANSWER; AND THEY APPEARED TO IGNORE US AT THAT POINT; AS THEY NEVER DIRECTED US TO SWITCH TO GND CTL. WE THEN CONTACTED GND; AND AFTER 3 CALLS WERE FINALLY GIVEN TAXI INSTRUCTIONS. I AGAIN QUERIED GND REGARDING THE HELI OVER OUR RWY. THEY ONCE AGAIN APPEARED TO IGNORE OUR CALLS. FINALLY; WHILE HOLDING SHORT OF RWY 4 TO CROSS AT TXWY C; AND AFTER WAITING MUCH LONGER THAN NORMAL TO CROSS THAT RWY; WE CONTACTED GND AND ASKED IF WE WERE GOING TO BE CLRED TO CROSS ANY TIME SOON. THEY FINALLY CLRED US ACROSS RWY 4; AND TO TAXI TO THE FBO. AFTER WE CROSSED RWY 4; AND ON THE TXWY TO THE FBO; WE ASKED GND CTL THE PHONE NUMBER TO THE TWR TO QUESTION THEM ABOUT THE HELI. THEY PROCEEDED TO GIVE US THE VHF FREQ (ALMOST AS IF THEY KNEW WHY WE WERE WANTING THE NUMBER).