Officers say the women were shot at about 1:30 a.m. Sunday at the Mai Thai Restaurant and Bar on Laurel Hill Avenue.
Their names haven't been released.
Police say both women were taken to Backus Hospital, where one of them died and the other was treated for injuries that didn't appear to be life-threatening.
The state police Eastern District Major Crime Squad is helping Norwich police with the investigation. The suspect hasn't been identified.
Anyone with information is urged to call Norwich police.
The woman's death is the first homicide of the year in the city.
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