# Tobit model with t-distribution

I've got a question concerning the estimation of a tobit model with the AER package in R. I observed t-distributed residuals, so that the assumption of normal distributed std errors is violated. Fortunately it's possible to choose "t" as the distribution when fitting with tobit(). It is tobit(<formula>, dist="t"). After changing the distribution from t to normal, the AIC increases, so this seems to be a good idea.

My problem is: Is it possible to flip the normal distribution that way? Is it still a tobit model and do I have to care about something when changing the distribution in a tobit model?

I appreciate any thought!