Gotta run?

I heard people said "Gotta run". that means he is leaving. why use past tense for "got"?

"Gotta run" is short for "I have got to run." I'm not sure what the history of this phrasing is, but that's what it means...

Actually the phrase's origins is more suitably explained by the bastardization of got, ie its colloquial substitution for the verb 'have'. It is not uncommon to hear, in very informal settings, things such as 'I got me some oranges'. The phrase in proper English would be 'I have some oranges'. This bastardization of the usage of 'got' has translated to its usage as replacement for 'have' in its capacity as an auxiliary verb. 'Gotta run' is short for 'I got to run' which in proper English is 'I have to run'.