The Department of Transportation permit alows illegal parking only while responding to an emergency. This has been discussed before in the Coffee Room with someone citing the exact regulations. If you have any doubt, however, check with the the DOT Authorized Parking and Permits Bureau.
Here’s a excerpt from Rudy Giuliani’s statement when he authorized the DOT to issue the permits:
Specifically, this bill will enable volunteer ambulance personnel to station their emergency ambulance service vehicles in close proximity to their work or home location, by permitting them to park in spaces that are prohibited by sign or rules, but only when the vehicle is on standby for an emergency ambulance service. The permit system does not and would not authorize the parking of motor vehicles in areas that would be contrary to public safety, such as fire hydrants or fire zones.
This permit system plays an important role in saving people’s lives in New York City. By allowing volunteer ambulance personnel to station vehicles near their home and work while on call for emergency service, the response time it takes EMTs to reach victims of medical emergencies is clearly improved.