KINGAIR BE200 HAS DOOR WARNING WHILE INFLT AND DIVERTS.

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PASSING APPROX FL200; WE GOT A CABIN DOOR WARNING LIGHT. I IMMEDIATELY STOPPED CLBING THE ACFT; AND BEGAN A DSCNT; TO REDUCE THE PRESSURE DIFFERENTIAL ON THE DOOR. WE ADVISED ATC OF OUR INDICATION; AND ASKED FOR A LOWER ALT. WE MAY HAVE SPECIFICALLY REQUESTED AN ALT OF ABOUT 8000 FT OR 10000 FT. I CAN'T REMEMBER EXACTLY. REVIEWING OUR POS; ALT; AND DISTANCE REQUIRED TO MAKE A DSCNT FROM FL200; I ELECTED TO CONTINUE NORTHWARDS; AND DECIDED THAT PSM WAS THE BEST ALTERNATIVE DEST; AND SO ADVISED ATC THAT WE WOULD LIKE TO DIVERT THERE. DURING THE DSCNT; THE COPLT PULLED OUT THE CHKLIST; AND WE RAN THROUGH ALL THE ITEMS. AT ONE POINT; DURING THE DSCNT; WHICH WAS ACCOMPLISHED AT APPROX 1500-2000 FPM; ATC ASKED US TO VERIFY THAT WE WERE HAVING A PRESSURIZATION PROB; AND I ANSWERED IN THE NEGATIVE; AND CLARIFIED THAT WHAT WE WERE EXPERIENCING WAS AN ANNUNCIATOR; AND THAT THERE WAS IN FACT NO INDICATIONS OF ANY OTHER PROBS ASSOCIATED WITH THE PRESSURIZATION SYS. ALSO; DURING THE DSCNT; THE CABIN DOOR ANNUNCIATOR EXTINGUISHED; I NOTED THAT IT DID SO AT APPROX 2.0 DIFFERENTIAL; I DON'T REMEMBER WHAT ALT THAT WE WERE AT THE TIME. I ELECTED TO CONTINUE MY APCH INTO PSM AND LAND SO AS TO HAVE AN OPPORTUNITY TO PERSONALLY INSPECT THE INTEGRITY OF THE DOOR. WE ACCOMPLISHED AN UNEVENTFUL; NORMAL APCH AND LNDG AT PSM; WITH THE ANNUNCIATOR EXTINGUISHED. AFTER CLRING THE RWY; I EXITED THE COCKPIT; AND WENT BACK TO CHK THE DOOR. THE CHK REVEALED THAT ALL 4 BAYONETS WERE IN THE CORRECT POS; THE LOCKING LATCH WAS IN ITS CORRECT POS; AND THE SWITCH WAS IN CONTACT WITH THE LOCKING LATCH. I OPENED THE DOOR TO VERIFY THE ANNUNCIATOR LIGHT WAS STILL FUNCTIONAL; AND IT WAS. I RECLOSED THE DOOR; AND NOTED THAT THE ANNUNCIATOR EXTINGUISHED. AT THAT TIME; I CONSIDERED THE DOOR TO BE IN A FULLY FUNCTIONAL CONDITION; AND THUS; THAT THE AIRPLANE WAS IN A FUNCTIONAL CONDITION; SO I ELECTED TO CONTINUE THE FLT. THE REMAINDER OF THE FLT WAS CONDUCTED WITHOUT INCIDENT. THE PROB; AND FAILURE WAS IN COM BTWN MYSELF AND THE COMPANY; IN THAT I DIDN'T ADVISE THE COMPANY OF THE EVENT; AND ELECTED TO CONTINUE THE FLT ON MY OWN INITIATIVE. ONCE I HAD TOUCHED DOWN; I HAD DEVIATED FROM THE PLANNED FLT DUE TO A MECHANICAL PROB; AND SHOULD HAVE RPTED THE INCIDENT TO THE OPS DEPT; AND GOTTEN THEM INVOLVED IN THE DECISION MAKING PROCESS; SINCE THEY ARE MUCH MORE EXPERIENCED AND FAMILIAR WITH PROCS THAN I AM. I HAVE SINCE BEEN ADVISED THAT A PRECAUTIONARY LNDG TO CHK ON AN ITEM IS IDENTICAL TO A MECHANICAL FAILURE AND THAT AS A PLT; I DO NOT HAVE THE AUTH TO CONTINUE FROM A DEV ON MY OWN WITHOUT AN APPROVAL FROM APPROPRIATE SOURCES WITH THE APPROPRIATE AUTH.