I think it is a Cooper's Hawk. Provided that is indeed a pigeon, it is certainly too large for a Sharp-shinned Hawk, its close but smaller relative. Let's see what others say.
I agree with you, Denis.
Cooper's Hawk, size suggests female. Can you provide an exact location?
It was in St. Stephen , NB .
An exact location would be a civic address, GPS points or proximity to a known as well as easily observed landmark. This information is not important. I was mostly curious, and as an area resident, I might look for the bird during my regular visits to town. This could be a wintering bird (most likely) or a local nester.
It was near the hospital .
Thanks. That is very helpful.