If it is a Manhattan coop it is unlikely that it can be rented to you without board approval and probably an interview. If it is a condo it is possible that an owner could rent to you without restriction. If it is a small building like a brownstone or townhouse it is possible that there is an owner of the building but there needs to be a superintendent (caretaker) listed at the building or nearby. If it is a larger building the owners will most likely employ a management company. (Also if the home is in Brooklyn or Queens or the Bronx it could be a private home and they may not have the same requirements of posting the super's contact info)
Here is a link to info from NY state about apartment renting:
Licensed Manhattan Real Estate Broker & Brokerage
"The Upper West Side's Buyer Broker"
331 Columbus Avenue, New York, NY 10023
Office: 212 721-3301 Email: firstname.lastname@example.org
Go to the building talk to the super and get the contact information for the management company. Talk to them for confirmation of ownership. Do not send any money to anyone until you have seen the apartment and verified the ownership and his right to rent.
Fran and Mark Redding
Prudential Fox & Roach, Realtors
1010 stonyhill Road
Yardley, PA 19067