The tenants of the 17-story building claim that the structure has degraded to an unconscionable degree, resulting in an unhealthy and unsafe living environment.
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Under federal housing laws, landlords must provide habitable environment free of contaminants, vermin and structural problems.
"You don't have to be an attorney to know that the housing maintenance code is not optional," Urban Justice Center attorney Marie Tatro told a local ABC News affiliate.
Forty-seven of the building's tenants have joined the lawsuit filed last week with the Bronx housing court, with tenants hoping the court will force University Residence to make all required repairs.