A police news release says the incident occurred around 8:45 p.m. Thursday in north-central Omaha.
Officers had been dispatched to the home of Madonna Runco. Runco told them her daughter was playing music too loudly in the garage and said the woman, Paula Moen, had a mental illness.
The officers say Moen pulled a knife when they asked her to turn down the music. One of them fired an electronic stun gun at Moen, but it proved ineffective.
The officers say Moen then pointed a flare gun at one of them. One officer fired her handgun, hitting Moen in the chest.
Moen was reported in critical condition at an Omaha hospital.