She shares first place with Mari Chun and Julieta Granada, who shot identical even-par 71s on Tuesday to remain at 4 under for the tournament.
Park is attempting to capture medalist honors for the third straight year after winning the Girls' Junior in 2002 and finishing second in 2003. The feat has been accomplished just once in the 56-year history of the championship, by Brandie Burton (1987-89).
'That would be really big for me,' Park said. 'But there are a lot of really good players out here, so it's tough.'
Defending champion Sukjin-Lee Wuesthoff struggled to a 4-over 75 to fall into a tie for sixth place at even par. Wuesthoff was tied with Granada, Chun and Jennie Arseneault for the lead after Monday's first round.
Wuesthoff is appearing in her sixth U.S. Girls' Junior Championship. Last year, she came back from a five-hole deficit to win the title at Brooklawn Country Club in Fairfield, Connecticut.
Arseneault shot a 3-over 74 on Tuesday and stands alone in fifth place at 1-under par 141. Paula Creamer is one stroke behind the leaders at 2 under after a two straight rounds of 70.