At surface level, Tippit and Oswald seem to have some sort of unusual connection. After the assassination, from the Gloco gas station, Tippit was watching as Oswald came over the Houston street viaduct in Whaleys cab. Tippit then immediately sped off according to the witnesses there. There is suspicion that Tippit may have been the one that honked the horn outside Oswalds house. Just after 1pm Oswald went into the Texas Theatre. Around the same time, Tippit made a phonecall from the Top Ten Records Store across the street.
Several anonymous calls were made to the DPD advising that someone suspicious had entered the Texas Theatre. This is unusual in itself because it should not be immediately obvious to anyone in the street that a man had entered the theater and not paid. Could Tippit have anonymously phoned in Oswalds location? And then drove around Oak Cliff pretending to not know where Oswald was, and got shot on a completely unrelated call. This would mean Oswald shot Kennedy, but there is some unknown relationship between Oswald and Tippit.
What was Tippit even doing at the Gloco gas station so far away from his assigned district 78. That is like a 20 minute drive away.