Where the defendant-hospital contracted with the City to provide medical care to persons incarcerated at the City's detention facility, it is considered a municipality for purposes of a 42 USC § 1983 analysis. A municipal defendant is subject to statutory liability for deliberate indifference to medical needs only where the alleged injury results from the execution of an unconstitutional policy or practice.
Smith v. St. Barnabas Hosp., NY Slip Op 07189 (1st Dep't October 25, 2018)
Here is the decision.