There is a 20% chance for Tri Attack to inflict a status. If this is rolled, poison, burn, and freeze all have an equal chance of being inflicted (~33.3% each). This results in any given Tri Attack having a ~6.7% chance to inflict a specific status condition.
This is only true starting in Generation II. In Generation I, Tri Attack cannot inflict status.
Tri Attack (Bulbapedia)