Officers pulled Rodriguez over early on Dec. 1 after spotting her black Mercedes allegedly weaving down Pali Highway in the Honolulu-bound lanes from Kailua.
Another "Lost" star, Cynthia Watros, was arrested 15 minutes later on the same road when police saw her car also moving erratically.
Both allegedly failed sobriety tests. Rodriguez had a blood alcohol level of 0.145, nearly twice the legal limit of 0.08, according to documents obtained by KITV-TV.
KITV quoted court and police documents that said Rodriguez was "very argumentative" and kept interrupting the officer who was explaining drunk driving sanctions to her.
"I don't (expletive) belong here! Why don't you just put a gun to my head and shoot me! You've already taken my freedom! You might as well take my life too!" she said, KITV reported Friday.
The officer who took Rodriguez in a police car to the Kailua substation quoted her as saying "Just take my car and I'll walk all the way to the North Shore but don't leave me in the back of this car poppie."
Rodriguez' lawyer declined comment.
The actress plays police officer Ana Lucia on the hit ABC drama series filmed in Hawaii.