If the original lease required you to pay for air condition maintenance, that carries over to your month by month tenancy. Otherwise, you are not required to do so.
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Dear Brooklyn NFP commercial tenant:
New York does not have a statutory bill of rights for commercial tenants. There is no warranty of habitability for commercial tenants. New York allows commercial landlord and tenants to negotiate their own contracts. When a landlord breaches a specific obligation to perform, the tenant has few options, all may involve a lawsuit, or ending the lease, and likely paying to fix the AC will be less expensive and disruptive.
Your expired written lease continued into the month to month tenancy. The initial review should look for the terms and conditions contained in the lease relating to the maintenance of the AC unit built into the office space. There should be some mention about the party, landlord or tenant, who carries the burden of the expense for the maintenance and repair. If the lease is silent, then the tenant may end up paying for the repair.
If necessary, consult with an attorney.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
Can they require us to pay for the maintenance and repairs? Yes.
You need to review the terms of the lease, the expiration of the lease only means your tenancy is month to month, the other terms of the lease survive. If the lease said the tenant is responsible for maintenance, then you are.