SMT DEPARTS ARPT AND IS ACCUSED BY ATC OF VIOLATING AIRSPACE.

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ON NOV/MON/91 PLT DEPARTED RWY 9 AT KEY W INTL ARPT AT XX45 PM LCL TIME. DURING TAXI PLT ADVISED GND THAT HE WOULD BE FLYING ALONG THE FLORIDA KEYS TO FT LAUDERDALE EXECUTIVE ARPT. (KEY W TWR AND THE NAVAL AIR STATION AT KEY W COORDINATE ALL ARRS AND DEPS). BOTH GND AND TWR ADVISED PLT TO MAKE A R TURNOUT AFTER TKOF. AFTER TKOF; AT END OF RWY; PLT TURNED R (SBOUND) AND WAS GIVEN LCL TFC LOCATION. KEY W TWR INSTRUCTS PLT TO CONTACT NAVY TWR (DEP) ON 124.45 AND ADVISED NAVY 'WITH YOU CLBING THROUGH 1500'. NAVY GIVES PLT SQUAWK CODE XXXX AND IDENT INSTRUCTIONS; PLT COMPLIES. AFTER REACHING POINT 5 MI S OF NAVAL AIR STATION PLT TURNS NE TO PROCEED ON HIS PRIOR DECLARED COURSE ALONG KEYS TO FXE. NAVY CTLR RESPONDS NEGATIVE MODE C AND REQUESTS POS; PLT RESPONDS 5 MI S OF NAVY AIR STATION. CTLR THEN STATES PLT HAS 'VIOLATED' HIS 'AIRSPACE' WITHOUT 'PERMISSION' AND REQUESTS CALL NUMBERS AND HOME BASE OF PLANE. PLT SO ADVISES. CTLR NEVER GIVES ANY FURTHER INSTRUCTIONS TO PLT; SHORTLY THEREAFTER RADAR SVC IS CANCELLED. PLT BELIEVES HE DID NOT VIOLATE 'NAVY' AIRSPACE AND WAS IN PROPER CONTACT WITH NAVY AT ALL TIMES. SOMEHOW; COORD BTWN KEY W TWR AND NAVY DEP CONCERNING PLT'S DEP BROKE DOWN. NAVY WAS UNABLE TO LOCATE AND MAKE INITIAL RADAR IDENT OF PLT AND MY LOCATION. PLT HAS MADE SAME DEP FROM KEY W ON NUMEROUS OCCASIONS OVER PERIOD OF YRS. THIS WAS THE FIRST TIME ANY SUCH 'AIRSPACE' PROBLEM OR 'COM' PROBLEMS OCCURRED. NAVY CTLR RESPONDED AS THOUGH PLT JUST 'DROPPED OUT OF THE SKY' INTO HIS 'AIRSPACE' AS OPPOSED TO A STANDARD KEY W DEP ALONG FLORIDA KEYS! BETTER COM BTWN KEY W TWR AND NAVY DEP REF DEPS FROM KEY W WOULD AVOID THIS PROBLEM IN THE FUTURE.