Typically, NFL commissioner Roger Goodell reviews all legal issues for possible discipline under the policy. But for the extent of the lockout, there is, by definition, no collective bargaining agreement and thus no personal-conduct policy.
An NFL spokesman told the Star Tribune that the case would be reviewed after the lockout, but I wonder whether the NFL Players Association would have to agree to grandfather in any issues that occurred during the dark period. I don't know if we can be certain that this incident would qualify as a "first offense" for Cook, either.
Regardless, Cook is the second Vikings players to be arrested this offseason. Defensive end Everson Griffen was arrested twice in January.