Witherspoon, 37, was arrested early Friday after quarreling with police who stopped her husband, talent agent James Toth, on suspicion of drunken driving, Hollywood magazine Variety reported on Sunday.
In a statement released late Sunday, the American actress said she could not comment what happened, citing legal reasons.
"But I do want to say I clearly had one drink too many and I am deeply embarrassed about the things I said," Witherspoon said in the statement published in full on celebrity website TMZ.
"It was definitely a scary situation and I was frightened for my husband, but that was no excuse. I was disrespectful to the officer who was just doing his job. I have nothing but respect for the police and I am very sorry for my behavior."
The incident occurred early Friday when Toth, 42, was pulled over when he drove across a double line on the road, Variety said citing the police report.
Appearing disheveled and smelling of alcohol, he then failed a blood-alcohol breath test, according to the report.
Witherspoon was warned to stay inside the vehicle but after her husband's arrest, she got out of the car and said, "she was a 'U.S. citizen' and that she had the right to 'stand on American ground,'" according to Variety.
Witherspoon was arrested on suspicion of disorderly conduct.
The magazine, citing the arresting police officer's report, said the actress asked if he knew who she was, saying: "You're about to find out who I am. ... You're going to be on national news."
The couple was released from custody at about 3:30 a.m. on Friday and were scheduled to appear in court on Monday, but sources told Variety that their attorney is expected to request a later date.
The couple married in 2011 and have a son together. Witherspoon has two children from her first husband, actor Ryan Phillippe.
(Editing by Doina Chiacu)