Yes definitely, you can apply for MBA in Anna University as there is no such rules for not getting admission if you are a non resident of Tamil Nadu.

Hi! you have to appear for TANCET exam in order to get admission in Anna university. Residency doesn't effect it's admission process. In order to get into anna university, one must have a full bachelor degree of three years with a minimum of 50% aggregate. Hope this helps!

Thank You!