A CE500 ENG DEVELOPED AN OIL LEAK; LOW OIL PRESSURE AND WAS SHUT DOWN IN FLT. OIL WAS ADDED AND THE ACFT WAS FLOWN TO THE NEXT DEST WHERE MAINT GROUNDED IT.

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THE TRIP WAS SCHEDULED TO LEAVE ZZZ1 TO ZZZ2 TO PICK UP 2 PAX TO ZZZ3. I PERFORMED PREFLT INSPECTION AT ZZZ1 AND EVERYTHING LOOKED NORMAL; EXTERIOR AND INTERIOR. STARTED THE SECOND LEG OF THE TRIP AT XA00 UNDER IFR FLT PLAN; VMC CONDITION. WITHIN 150 NM FROM ZZZ3 AT FL370 MY FO AND I NOTICED THE L OIL PRESSURE GAUGE IS INDICATING IN THE LOWER GREEN ARC. SEVERAL MINS LATER; THE L RED LOW PRESSURE LIGHT ILLUMINATED WITH THE PRESSURE GAUGE CONTINUOUSLY BUT SLOWLY DROPPING BTWN 35 PSI-70 PSI. THE L OIL TEMP WAS SLIGHTLY HIGHER AGREEING WITH THE PRESSURE GAUGE. FOLLOWING THE CHKLIST WE REDUCED THE PWR ON THE L ENG AND CLOSELY MONITORED THE GAUGES. THE PRESSURE CONTINUED TO DROP BELOW 30 PSI IN VMC CONDITION AND I DETERMINED IT SAFE; FOLLOWING THE CHKLIST; TO PERFORM A PRECAUTIONARY SHUTDOWN. I ADVISED APCH OF THE SITUATION AND CONTINUED THE LAST 50 NM SINGLE ENG TO THE ARPT AND WAS CLRED FOR THE LNDG. AFTER LNDG; I CHK THE OIL IN THE L ENG AND NOTICED THAT THE DIPSTICK DID NOT REGISTER ANY OIL. IMMEDIATELY I CALLED THE OPS OFFICER AND DIRECTOR OF THE MAINT TO INFORM THEM OF THE SITUATION INCLUDING THE PRECAUTIONARY SHUTDOWN. THEY BOTH RECOMMENDED TO ADD ENOUGH OIL TO THE PROPER LEVEL; RUN THE ENG FOR 5-10 MINS AND CHK THE OIL LEVEL AND CONTACT THEM WITH THE RESULT. AFTER ADDING AND RUNNING THE ENG IT SEEMED THE OIL LEVEL STAYED THE SAME. I INFORMED BOTH THE OPS OFFICER AND THE DIRECTOR OF THE MAINT OF THE RESULT AND WERE RELEASED TO CONTINUE TO OUR NEXT DEST; NO PAX; AND WAIT FOR FURTHER INSTRUCTION AT ZZZ4. ONCE AT ZZZ4 I CHKED THE OIL LEVEL AND NOTICED IT WAS LOWER THAN BEFORE OUR DEP FROM ZZZ3 CONFIRMING THE LOW OIL PRESSURE; SLIGHTLY ABOVE 70 PSI; DURING OUR FLT TO ZZZ4. THE SITUATION WAS EXPLAINED TO THE OPS OFFICER AND THE DIRECTOR OF MAINT WHICH THEN THEY DECIDED TO HAVE AN AUTH CESSNA REPAIR SHOP TO INVESTIGATE THE PROB. AFTER REPLACING A SEAL WHICH WAS THOUGHT TO BE THE PROB AND A MAINT FLT THE OIL LEAK STILL PERSISTED AND THE HEAD MECH AT THAT POINT DECIDED TO DEEM THE PLANE NOT AIRWORTHY AND GNDED IT FOR FURTHER INVESTIGATION. IT IS NOTEWORTHY THAT THE OPS OFFICER CRITICIZED ME AND MY FO FOR SHUTTING DOWN THE ENG AND ATTRIBUTED THAT TO OUR LACK OF EXPERIENCE. THE DIRECTOR OF MAINT CLRED US TO FLY TO OUR NEXT DEST WITHOUT CONSULTING WITH PRATT AND WHITNEY MANUAL TO DETERMINE WHETHER WE SHOULD FLY AFTER A PRECAUTIONARY SHUTDOWN OR THE ACFT SHOULD BE GNDED FOR FURTHER INVESTIGATION. IN THE FUTURE ANYTIME I PERFORM A PRECAUTIONARY SHUTDOWN DUE TO ANY MALFUNCTION; I WOULD NOT FLY THE PLANE UNTIL I AM GIVEN A FERRY PERMIT SIGNED BY OUR DIRECTOR OF MAINT OR ANOTHER MECH APPROVED BY THE OPS OFFICER AND DIRECTOR OF MAINT AS OPPOSED TO THE VERBAL PERMISSION BY THEM.