Swamy and Mahtab will represent opposition-backed candidate P A Sangma on the issue before the CEC.
Sangma and his camp are not satisfied with the verdict given by Returning Officer V K Agnihotri. After a meeting here on Thursday, Sangma's Election campaign committee has decided to take the matter to the CEC.
The RO had said he was convinced that Mukherjee had quit as Chairman of Indian Statistical Institute on June 20 as claimed by him. BJP maintains Mukherjee's signature on his resignation letter is fabricated.
"We are going to the CEC with the complaint as under Article 324 of the Constitution, the authority of superintendence of polls lies with the EC," BJP leader S S Ahluwalia had told PTI on Thursday.
"The order of the RO is not complete in itself. All disputes and issues which we had been raised should have been dealt with by the RO as per Rule 5(E). But the RO has gone by the advise of Mukherjee's representative (Pawan Bansal) that this should be dealt with under Part III of the Constitution on President and Vice-President," he said.