Our refrigerator has been broken for a week

Im not sure but I think a landlord is only required to provide a stove and/or refridgerator. I think Mulitple Dwelling is 3 or more units so I am not sure which category you fit into. You can also check out www.tenant.net

I found this in the NYT archives:

Q I have a friend who lives in an apartment in the West 30's that I believe is rent-controlled. He has been there for more than 15 years and has had no stove for the entire time. Is the landlord required to provide a stove? . . . Jennifer Williams Ketay, Manhattan.

A Jeffrey Ween, a Manhattan landlord-tenant lawyer, said that both the New York City Housing Maintenance Code and the state's Multiple Dwelling Law require a landlord to provide gas or electricity for cooking facilities, but neither requires the landlord to provide the appliances themselves.

Mr. Ween added, however, that under both rent control and rent stabilization, any services provided by a landlord at the time an apartment became subject to regulation must be maintained even if there is a change in occupancy. Accordingly, he said, if there was a stove in the friend's apartment at the time the apartment became subject to regulation, the friend is entitled to a stove now, even if he accepted the apartment without one.

Mr. Ween said that since information regarding the services provided in specific rent-regulated apartments is kept on file with the State Division of Housing and Community Renewal, the friend should contact the division to determine what is on file for the apartment.