The general rule is that a hospital may not be held vicariously liable for the acts of a physician who is not an employee of the hospital, but, instead, is one of a group of independent contractors. However, a hospital may be vicariously liable if a nonemployee physician acted as its agent, or if it exercised control over the physician.
Castro v. Durban, NY Slip Op 03503 (2d Dep't May 17, 2018)
Here is the decision.