The Supreme Court agreed yesterday to decide whether the federal government must pay relocation benefits to tenants it ordered to vacate the deteriorating Sky Tower apartment complex at Wheeler Road and Wahler Place SE.

A divided U.S. Court of Appeals for the District of Columbia ruled last November that the Department of Housing and Urban Development must pay the benefits because the tenants are "displaced persons" under a 1970 federal law involving takeovers by HUD of a project after its sponsors have defaulted on the mortgage.

In a similar case from Indianapolis, the 7th U.S. Circuit Court of Appeals reached a conflicting conclusion. So have two other federal appellate courts. To resolve the conflict, the Supreme Court will bear argument in the two cases in the term starting in October.

The law at issue - the Uniform Relocation Assistance and Real Property Acquisition Policies Act - authorizes up to $4,000 in "replacement and housing" payments to persons ordered to move from a federally added project by the agency that acjuires it.

Built in the 1950s, the 19-building Sky Tower complex contained 217 small garden apartments. In 1970, a nonprofit corporation bought Sky Tower, tried to rehabilitate it by converting the apartments into larger ones for low-and moderate-income families and received HUD financial aid.

The effort failed. After the original contractor defaulted on rehabilitation work, HUD took the unusual step of permitting an increase in the size of the insured mortgage and getting a new contractor.

But the second contractor also abandoned the job. Finally, in June 1973, HUD took title to the complex, hired a managerial firm to operate it and arranged new month-to-month leases on the previously existing terms.

Later, the department decided that further efforts to rehabilitate Sky Towers would be futile and decided to demolish it and sell the land. In September 1974 the management firm gave notice to vacate to the 72 remaining families. Those who were current in their rent payments were allowed $300 for moving expenses and given free occupancy in their final month. Fifty-five families vacated.

A group of tenants then filed a suit in U.S. District Court challenging the decision to raze rather then rehabilitate Sky Tower. One of their claims was that HUD had failed to pay them "displaced persons" benefits.

The court barred further evictions or demolition and ordered HUD to rehabilitate certain buildings and to offer tenants who had moved out the opportunity to move back in. Eighteen of the 55 families who had left returned.

The court also allowed prorated benefits of about $750 each to the 37 families who vacated in response to the department's September 1974 notice. The covered period ended Aug. 1, 1975, when the court permitted their return.

The appeals court affirmed only in part, holding that the tenants who left in compliance with HUD's notice were "displaced persons" entitled to full benefits, and that the 18 families who could have returned but did not also were entitled to full benefits.

In late 1976, meanwhile, a settlement was reached under which the District of Columbia would take title to Sky Tower and HUD would provide substantial subsidies for it to continue in operation. After that, tenants complained that deterioration continued.