A CRJ200 Captain reported during pushback his aircraft started rolling free when the towbar separated from the tug.

Narrative

During pushback and while starting the #2 engine; I looked up to notice that the tug pushing us back was stopped and the aircraft was continuing to move backwards. The ground crewmen on the tug was waving his arms and signaling for me to apply the brakes. I applied the brakes and brought the aircraft to a complete stop. Looking at the tug is appeared that the towbar had not been correctly attached to the tug's pinnel hook. The towbar was still attached to the aircraft. We rolled approximately 15-20 FT away from the tug before I stopped the airplane. Since the towbar was correctly attached to the aircraft and after speaking to a ramp supervisor on headset outside of the aircraft; we determined that no further action was required and continued the flight normally. Ground crew incorrect attachment of towbar to tug. Oversight perhaps due to being in a hurry for an on-time pushback. The First Officer completed a walkaround approximately 45 minutes before the event. He said he did not notice the towbar or how it was connected.