What was Rajinikanth’s last direct non-Tamil venture?

Aatank Hi Aatank, a Godfather rip-off^[1] that came in 1995, in which he co-starred with Aamir Khan. (No, it wasn't Pedda Rayudu^[2].)

[1] - He played Sonny, a tad unqualified.
[2] - Ref: RajiniKanth.com.

What was Rajinikanth’s second film as an actor? How is it connected to another Tamil film starring Rajini?

Katha Sangama, Puttana Kanagal’s multi-story film in Kannada, was Rajinikanth’s second film. It consisted of three independent stories and Rajinikanth played the lead in the third story, Munithayi.
As per Rajini’s request, this segment of the film was later adapted by Mahedran in Tamil as a full film, Kai Kodukkum Kai.