Deputies were called to a home on Wendel Street around 1 a.m. Thursday.
They arrived as the suspect was leaving the house. Deputies say he climbed into a red Jeep and led them on a short chase.
He jumped out of the vehicle at some point, ran and went into the bayou.
Officials say he went underwater and never came back up.
HPD dive teams were alerted but it's not clear if they were able to search for him due to the strong current.