Both incidents occurred in the early hours of Sunday and Monday, October 29 and 30.
The Richhill incident took place around half past midnight on Monday in the Victoria Court/Maynooth Road area of the village. The woman was assaulted by a man at her home and suffered a number of injuries.
Police would like to hear from anyone who saw a sporty, white BMW driving in the area or witnessed anything unusual around this time. Phone police on 101 and quote reference 49 30/10/17.
Between 12.30am-1.30am on Sunday, a woman was assaulted by a male intruder when she returned to her house in Railway Street, Armagh.
Detective Inspector Lynne Knox said police are not linking the incidents at this time but she said they would like to hear from members of the public who may have information.