Park, the South Korean star who swept the first three majors of the season and has six LPGA Tour victories this season, had seven birdies and two bogeys at Royal Mayfair to match Kerr at 8-under 132.
Kerr, coming off the United States' loss to Europe in the Solheim Cup, shot her second straight 66. She won the Kingsmill Championship in May for her 16th career LPGA Tour title.
Angela Stanford and France's Karine Icher were a stroke back. Icher had a 66, and Stanford shot 68.
Defending champion Lydia Ko was 6 under after a 69. Last year at Vancouver Golf Club, the amateur became the youngest winner in LPGA Tour history at 15 years, 4 months.