Rosie Jones fired a 7-under 65 to join Jenna Daniels in a tie for fourth at 8-under-par 136.
Kung, who earned her second victory of the season last week at the Wachovia LPGA Classic, held the opening-round lead but quickly found herself moving backward under rainy conditions at The Rail Golf Club.
The 22-year-old played the back nine first and bogeyed each of her first two holes to fall back to minus-6. It wasn't long before Kung recovered, however, and she collected three birdies over her next seven holes to make the turn at 9-under.
'I just kept playing,' said Kung. 'I was not hitting the ball as well as yesterday, but kept playing. I told myself there is a lot of golf to be played at this tournament and it all came around after a few holes. I didn't know what happened to me on the first two holes. Those two shots were weird.'
Kung hit a pitching-wedge inside two feet for a birdie at the second and left her second shot short at the par-5 fourth. Kung chipped to a foot and tapped in for the birdie before knocking an 8-iron to 10 feet for a birdie at the eighth.
At the par-4 ninth, Kung landed her approach within six feet of the cup and ran home the putt for her seventh birdie of the day.
'The greens are soft out there,' said Kung. 'You are able to go for the pin and I was able to hit it close and made a lot of six-footers.'
Han, who is a two-time winner this season, also started on the back side and tallied three birdies and two bogeys over her first nine holes.
The 25-year-old two-putted for a birdie at the fourth and dropped her tee shot inside eight feet for a birdie at the par-3 fifth en route to a round of 69.
Rosales went around without a bogey and picked up five birdies to join Han at 9-under-par 135.
'I am pretty happy with where I am,' said Rosales. 'There are still two more days, and it's anybody's ball game right now. I will just get out there and do the same things.'
Laura Davies carded a 67 to finish alongside Eva Dahllof and Pat Hurst at 7-under-par 137.
Becky Morgan, Karen Stupples, Jackie Gallagher-Smith and Leslie Spalding were one shot further back at 6-under-par 138.
Michelle McGann, who won this event in 1996, was part of a group at 5-under-par 139 that featured Se Ri Pak, Grace Park and Natalie Gulbis.
The 36-hole cut fell at 1-under-par 143 with 74 players qualifying for the weekend. Among those who didn't make the grade were Lorena Ochoa and Dottie Pepper.