Police had registered an FIR against the actor on December 5, charging him with falsifying and fabricating documents by showing an address in the Union Territory of Puducherry and getting the vehicles registered there, causing revenue loss to the Kerala government.
The FIR is pending before the Chief Judicial Magistrate Court, Thiruvananthapuram.
In his anticipatory bail plea, Gopi said the allegations prima facie were false.
The BJP MP said he owns agricultural land around Puducherry, which was being looked after by family members, including his brothers.
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He said he has a house at Bengaluru and his brothers have residences at Coimbatore and Tuticorin, so the vehicles were frequently used to ply within these states.
Gopi said the charges had caused great insult and annoyance to him, and this would be further eroded and worsened if he was arrested.
He said he was prepared to fully cooperate with the investigation team and at any time they wished to interrogate him.