Can New York City (or any other municipality in New York) be held liable in negligence for my personal injuries if they provided funding for, and retained the ability to oversee, the operations of the non-profit organization's property where I was injured?

As noted in our news section, if the sole basis upon which you seek to hold the City of New York liable for your injuries is a contract provision that affords the City a right to have general supervision of the services rendered by the non-profit, as well as the premises maintained by the non-profit, the claim will not survive, because that language alone is insufficient to prove that the City of New York should be held liable for their role in "controlling" the defective premises.