AN A320 TAXIING FOR TKOF AT RSW FOUND THEMSELVES IN THE MIDDLE OF A POLICE CHASE.

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THE FLT PUSHED BACK AND ON TAXI OUT WE HEARD A DISCUSSION BTWN THE TWR AND POLICE THAT SOMETHING WAS ON THE RWY AND THE POLICE WAS IN CHASE. THE TWR NEVER SAID ANYTHING ABOUT A VEHICLE AND NOR DID THE POLICE ON THE RADIO. WE BOTH ASSUMED HE WAS CHASING DOWN A LOOSE DEER OR ANIMAL ON THE RWY (FORT MYERS HAS HAD ALLIGATORS ON THE RWY BEFORE). NEXT; TWR STATED TO THE POLICE THAT HE NEEDED TO CLR THE RWY FOR A DEPARTING ACFT (HE WAS REFERRING TO US BUT WE WERE STILL ON THE RAMP ABOUT 500 YARDS SHORT OF THE TXWY). THE POLICE STATED SOMETHING TO THE EFFECT OF 'I CAN CLR THE RWY BUT I AM NOT SURE HE WILL LISTEN.' AT THIS POINT; I STILL ASSUMED WE WERE TALKING ABOUT AN ANIMAL ON THE FIELD SINCE THERE WAS NO URGENCY IN THE CTLR'S VOICE. AT THIS POINT; I TURNED ONTO THE TXWY HEADED NOSE W FOR RWY 6. WE WERE DOING OUR BEFORE TKOF CHKLIST WHEN TWR RESPONDED TO US 'BE ADVISED THAT THE VEHICLE PASSING YOU ON YOUR R NO ONE IS TALKING TO.' I LOOKED OFF THE R SIDE OF THE ACFT EXPECTING TO SEE AN ARPT VEHICLE DOING AN INSPECTION WHEN A VEHICLE CAME PASSING BY AT A HIGH RATE OF SPD. JUST THEN; THE POLICE VEHICLE PASSED US ALSO AT HIGH RATE OF SPD IN CHASE. THE VEHICLES SPED TOWARD THE FAR END OF THE RWY AT WHICH POINT I DECIDED TO STOP THE ACFT WHERE WE WERE UNTIL WE FIGURE OUT WHAT IS GOING ON. THE VEHICLE AND THE POLICE CAR TURNED BACK TOWARD THE ACFT AND HEADED FOR US ON THE TXWY; BOTH VEHICLES VEERED OFF TO MY R AND PASSED UNDER THE WING BUT I COULDN'T TELL FROM MY ANGLE. WE STAYED PUT AND SAW THE CHASE CONTINUE OUT ON THE RWY. ABOUT 3-4 MINS PASSED AND WE COULD NO LONGER DETERMINE THE LOCATION OF THE VEHICLE SO WE PROMPTED TWR TO GIVE US THEIR LOCATION. AFTER A FEW MINS; TWR CAME BACK ON THE RADIO STATING THAT THE SUSPECT HAD BEEN APPREHENDED AND THAT WE COULD CONTINUE OUR TAXI TO RWY 6 FOR DEP. I ASKED FOR A RWY INSPECTION TO VERIFY THAT NOTHING HAD FALLEN OFF THE VEHICLES DURING THE CHASE AND WAS LYING ON THE RWY. THE TWR HAD A VEHICLE RUN THE ENTIRE LENGTH OF THE RWY IN SEARCH OF ANY FOD. AFTER THIS; WE WERE CLRED FOR TKOF. IN RETROSPECT; IF I HAD KNOWN THAT THE THING LOOSE ON THE RWY WAS A VEHICLE WITH POLICE IN CHASE; I WOULD HAVE NEVER LEFT THE GATE. IT WASN'T UNTIL WE TAXIED CLOSE TO THE TXWY THAT WE REALIZED THAT THIS WAS A VEHICLE THAT WAS BEING CHASED DOWN.