According to the police report, obtained by TMZ, the officer on the scene asked Major to perform SIX field sobriety tests ... and she didn't pass a single one.
When asked to touch her finger to her nose, the report says ... "Major missed the tip of her nose on her second, third, fourth, and fifth attempts. Touching her nostril on her second, third, and fourth attempts, and touching the space between her nose and upper lip on her fifth attempt."
As for reciting the alphabet -- "On her first attempt she gave the sequence LMX twice and spoke at a really fast pace. On her second attempt she did not keep her eyes closed and got stuck on the letter V. Major was never able the recite the alphabet from A to Z."
Police say her BAC was .243 -- more than 3 times the legal limit. According to the report, she fittingly told police, "I know I have a drinking problem."
Major was arraigned on the DUI charge, plus a battery charge for the fight with Lohan. She'll be in jail until her next hearing ... on Tuesday.