9:00AM: The fledgling that was on Goddard Hall yesterday got inside one of the empty classroom's windows and was discovered by an NYU staff member around 2:30AM today. The staff member called security who called a park ranger friend of mine who went to the classroom and captured it.
He contacted the Horvaths of WINORR (Wildlife in need of Rescue and Rehabilitation) and reported the situation. He said the bird looked healthy and uninjured. WINORR advised him to keep the fledgling for observation and then to release it in the park if all seemed well.
The ranger invited me via text message to attend the release but since it happened very early in the morning (5:30AM), I was still asleep when all the action occurred.
I called the ranger as soon I got the message and he told me the fledgling was placed on a park lawn but it wouldn't fly away. The ranger said he couldn't just leave the bird there so he contacted the Horvaths again and they advised him to bring the bird to their wildlife rehabilitation center. The fledgling is with them now.
It turns out the fledgling isn't injured per se but is missing two of its primary flight feathers so that may be why it wouldn't fly away. The bird appeared healthy (bright, clear eyes and feisty and strong) but is being checked for any possible illness and will hopefully be released back into the park soon.
The ranger kindly allowed me to post these photos of the fledgling taken at the release attempt.
I have since heard from another source that the Horvaths wish not to be called on the matter as they have lots of rescues to attend to but this is fourth-hand information but a good tip nonetheless.
Location of the missing feathers (you can see the broken tips):