Police say they are investigating the shooting death of a woman wielding a meat cleaver on a California elementary school playground as a possible case of "suicide by cop."

Police on Wednesday identified the woman fatally shot as 43-year-old Elizabeth Catherine Kropp of Modesto.

Police Sgt. Brian Findlen says officers found Kropp hitting and cutting herself with the cleaver around 2 p.m. Tuesday. Two officers opened fire when Kropp charged them with the cleaver.

Authorities say a preliminary investigation suggests Kropp had a history of mental health issues. Findlen says several children were on the playground when Kropp arrived but were escorted inside before the shooting.