It was easy to get to from my resort - jump on the clockwise bus out the front, and hop off at Cook's Corner, where the bus stopped. The police station was right there, a two-storey white square box with countless rented scooters parked out front.
The reception area was dark and harboured half a dozen languorous backpackers. At the counter a typically full-figured Polynesian woman - dressed in the universal blue outfit favoured by police worldwide - wore an atypical grimace of indifference.
"Drivers licence?" she said in that slightly curious New Zealand accent they have, as though there would be no other reason to visit the police.
I was made to fill out a form stating the usual details: name, date of birth, where I was staying. I handed this over, together with my usual driver's licence, and $10, and was ushered into another dank room at the back.
She grabbed a Polaroid camera, and raised it as if firing a .38 pistol from the hip. The flash left me disoriented. "Give us 20 minutes," she said, which explained the numbers waiting out front.
Most were applying for scooter licences, which operate slightly differently.
First you rent your scooter, then ride it to the station to apply for the licence. An officer watches you go around the block behind the station and you're given the $10 stamp of competence.
I passed the time looking around the station, which more resembled the memorabilia and merchandise section of a Hard Rock Cafe than a law enforcement office. One entire wall was covered with souvenirs emblazoned with a rather funky Top Kopz logo.
What they lacked in grammatical precision they made up for with entrepreneurial opportunism. Baseball caps, T-shirts and rather snappy polo shirts for just $25.95.
The wall behind the counter was covered with a montage of blue-and-gold police badges and patches, mostly the sew-on type, mostly American. Reciprocal souvenirs from visiting coppers.
There was a small white card folder on the counter, saying: "Welcome to the Cook Islands."
In it were the Rules of the Road for Driving Safely, and my new licence, a small laminated grey rectangle, with the Cook Islands flag, and its circle of stars, front and centre, from which my half-dazzled and bemused visage beamed. A compulsory $10 souvenir.
I perused the list of enclosed rules, which dispensed more commonsense advice than stringent laws: "Watch for small children and their pets ... Please don't leave your keys in the car ... Don't be in a hurry, drive at a leisurely pace".
The speed limits are 40km/h in a restricted area and 60 km/h on the open road.
I bypassed Budget and Avis, plumping for Island Rent-a-Car which had advertised Jeeps and coupes from $40 a day.
Margaret, the charming assistant, in blue singlet and shorts sitting on a chair in the middle of a grass field, surrounded by cars, didn't know anything about that offer, but agreed to give me one of her low-cc sedans for that amount. I set off anti-clockwise along the outer road, almost reaching the speed limit in first gear, to recce the stunning island and get the lay of the land.
After following what was almost a perfect circle around the entire coral-ringed atoll for 50 minutes - turquoise water on one side and emerald mountains on the other - I was back at the same spot.
I had clocked up a whole 32km. And not encountered a single traffic light, let alone open road. The traffic was mainly scooters.
I studied the map. There was also an inner circle, the historic Ara Metua, built from volcanic slabs by Chief Toi in the 11th century. This was more varied, with papaya, guava and passionfruit plantations, and errant goats and chickens to swerve around.
Just over an hour later I was back again. I had done the island. Driven along every sealed kilometre.
By now, it was 35C. My recce had turned up the perfect place for a chilled Cooks Lager - Trader Jacks on the wharf at Avarua, a classic South Seas Bar.
Which reminds me of another thing. Although they have had breathalyser trials in Rarotonga, there is no drink-drive legislation. But maybe it won't be too long coming because 69 of the 144 motorists tested on the first night of trials were over the limit.
Perhaps that will encourage more tourists to take advantage of the $2.50 round-the-island bus service - you can go around four times for the same price as the licence.
There have also been mutterings by senior police about tightening controls on who is issued a licence in the first place, probably spurred on by tourists who think they're Licensed To Thrill.
There's only one thing I would change about driving in the Cook Islands. I don't begrudge them my $10. I just wish my souvenir licence photo had been taken after my week's holiday.
Stu Lloyd went to Rarotonga at his own expense.
