Angela Willis at Spillane's Towing and Recovery confirms that the driver is indeed towing the little moped. Willis wasn't sure why, but thought it was because the bike wasn't registered, and didn't have insurance.
A call to the Burlington PD didn't shed much light on the subject — the parking enforcement manager is out for the weekend. But the person who answered the phone said if you've got a motorized vehicle that has to be registered, you have to treat it like a car. In other words, don't park it on Church Street. That bike rack in the photo is just for people-powered vehicles.
*** UPDATE: Willis called back with new information — apparently the moped was not parked at all. The police pulled the driver over because the vehicle was weaving in traffic. The cops apparently checked up on the driver, and found the moped was not insured, or registered, hence the tow.