The incident happened in the Lower Market Street area of Downpatrick this morning, Thursday, June 12.
Just before 9.30am police on mobile patrol received a report that a woman was approached by an unknown male who attempted to wrestle her handbag from her.
During the struggle the woman sustained a head injury and an injury to her arm.
She has been taken to hospital for treatment to her injuries which are not believed to be life threatening.
It is not yet known how she sustained the injury.
The male left empty handed.
Detectives would ask anyone who may have witnessed this incident to contact them at Downpatrick CID on the non emergency number 101.
Or, if someone would prefer to provide information without giving their details they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.