Ciganda began the day three shots off the lead and dropped a further stroke behind with a birdie at the first, but fired eight birdies in an impressive six-under 66 to move level with Park, who rallied on the last five holes to end three-under.
The South Korean made 13 straight pars on a frustrating day of near misses and shaved cups, but picked up three late birdies, including a 10-feet gain on the final hole, to stay joint-top of the leaderboard.
Spaniard Azahara Munoz is two shots back after posting a second round 67, with world No 1 Ko joining Stacy Lewis, Karrie Webb and Jenny Shin a further stroke behind on six-under for the tournament.
Ko remains on course for a third consecutive tournament victory, despite dropping shots with a double-bogey six at the 13th and a bogey at 15th, with the 17-year-old finishing with back-to-back birdies in a two-under 70.
It was a frustrating day for joint-overnight leader Yani Tseng, who failed to register a birdie in a three-over 75 to fall six shots behind the leaders.
Second Round leaders:
-9 Carlota Ciganda (Esp)
-9 Inbee Park (Kor)
-7 Azahara Munoz (Esp)
-6 Jenny Shin (USA)
-6 Karrie Webb (Aus)
-6 Lydia Ko (Nzl)
-6 Stacy Lewis (USA)
-3 Yani Tseng (Tpe)
Level Lexi Thompson (US)