A man shot in the buttock by police in Cowra was allegedly chased through the streets of the central western NSW town after threatening police and residents with weapons over 40 minutes.

Dennis "DJ" Doolan, 32, sustained a single gunshot wound to his left buttock following the confrontation in Jindalee Circuit at 12.10pm on Wednesday.

A witness, Justin, posted a dramatic photo of the encounter on Facebook showing an officer pointing his firearm at an Indigenous man in a red T-shirt who appears to have his arms up and his back to the officer.

The photo immediately sparked fury among some Cowra residents and relatives of Mr Doolan, who accused the police of racism and threatened to protest.