Lindberg, the first-round leader, followed her opening 65 with a bogey-free 67 to join Park at 12-under 132 in the first women's major of the year.
American Jessica Korda (68) was best of the rest on nine-under.
Park said she had not even been aware of her score.
"I just was so focused on my game today," she told reporters via an interpreter.
"I was super focused at the U.S. Open, and felt just as focused for today's round.
"Today the shots were awesome. I just felt really good about my driver."
But it was a wedge that brought about the highlight of her day at the 15th, where her approach from 102 yards landed beyond the hole, took a couple of bounces and then rolled back into the cup.
"I just felt really good about the distance and saw that it had really great backspin, but I didn't even see it go in," she said.
Co-leader Lindberg has never won an LPGA event but hopes to make her first victory a major.
"I haven't let myself get frustrated that I haven't yet had the success that I wanted," said the 31-year-old.
"I just keep plugging away and improve year by year. I'm collecting so much experience, getting more and more ready to be in this situation and every time there feeling more comfortable."
American Lexi Thompson (72) struggled on the greens but almost holed her eagle approach shot at the last, tapping in for birdie to trail by eight shots.
Thompson last year lost to Ryu So-yeon in a playoff after incurring four strokes in penalties -- two for replacing her ball in the wrong spot for a tap-in putt and two more for signing an incorrect scorecard in the third round.
The violation was brought to the attention of officials the following day by a television viewer. In December, golf's governing bodies agreed they would no longer consider rules violations by fans watching events on television.
Thompson played the first two rounds this week with fellow American Michelle Wie (67), who made the cut after an opening 75 during which she suffered dizziness.
Wie joked after her first round that blurred vision had left her seeing several balls as she stood over some shots.
"I definitely saw one golf ball today, which was good," she said, adding that she had tried to conserve energy. "I sat down every chance I could.
"I just talked to the doctor last night, and he said it's definitely some kind of ear virus thing, and definitely having a little bit of vertigo going."
(Reporting by Andrew Both in Cary, North Carolina, editing by Pritha Sarkar/Peter Rutherford)
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