Exclusive

A troubling twist in the Jeff Hardy drunk driving arrest ... cops say the WWE star had a bloody nose during the stop and told officers it was from an earlier "fight" with his wife.

It's all spelled out in the police report, obtained by TMZ Sports ... which describes how the Carthage Police Dept. in North Carolina received a tip about a careless and reckless driver around 8:40 PM on October 3.

When cops found the car, they noticed the driver (Hardy) was parked in front of a liquor store ... and when he came out, he was carrying a case of beer.

42-year-old Hardy got into his car and began to drive while cops followed closely -- and finally pulled him over when they observed him weaving badly in his lane.

During the stop, the officer noticed Hardy had "what seemed to be dried blood on his nose" -- and asked what had happened.

"The driver advised that him and his wife got into a fight."

Surprisingly, the police report doesn't give any more details about the possible domestic violence incident ... instead the officer proceeds to question Hardy about alcohol.

Cops say Hardy admitted to taking 2 shots of vodka earlier in the night -- and he ultimately admitted to being impaired.

Cops also say Hardy bombed the field sobriety test -- and was uncooperative when asked for a breathalyzer or blood sample.

The officer ultimately got a search warrant from a judge to extract a blood sample from Hardy -- so EMS was summoned to draw it.

Hardy was booked for Driving While Impaired and Driving on a Revoked License. The police report lists Hardy at 6'1" and 175 pounds.