D.C. Mayor Marion Barry has decided to ask the City Council for authority to make blanket exemptions to the city's controversial residency law in the face of complaints by city officials that the live-in-town requirement is causing personnel shortages in many crucial job areas.

Barry's request, which will be introduced to the council by Chairman Arrington Dixon, would give the mayor authority to make exemptions to the residency requirement "whenever the mayor deems its to be in the best interests of the government of the District of Columbia."

Such an action would give the mayor broader discretion than would a similar request rejected last December by the council. At that time, Barry had requested only the authority to grant exemptions to hire computer programmers.

Alan F. Grip, the mayor's press assistant, said that in addition to a shortage of computer specialists, which he called a nationwide problem, the city also needs doctors and nurses in some specialty areas.

Under the law, newly hired city workers must become District residents within six months of their employment or lose their jobs. In rejecting the mayor's proposed exemptions last year, the council temporarily gave Barry authority to extend the six-month grace period by a total of three months.