Is it possible to become a tenure track Assistant Professor at the same university where I did Post Doc?
I think this might vary by institution, but for most, at least in the US, there wouldn't be any problem with such a move. Of course, you are unlikely to get any advantage in your application and regulations most places will require that you be treated like any other. 

I know of one situation like this in which the university really wanted to keep a post-doc so wrote the specification for the tenure track job that matched him nearly perfectly. Nearly everything except the Father's middle name. They sent out the required national search and got back three candidates (among many others) that seemed to be a better fit (on paper) than he was. But he got the job in the end. 

So, not impossible (most places) but likely no advantage either.