Emails and text messages are being sought from Bill Baroni, Christie's top deputy at the Port Authority of New York and New Jersey, who has resigned, and three others, including a top aide to agency chairman David Samson.
A state legislative panel has issued a total of 20 subpoenas, including to the governor's chief of staff and chief counsel.
A full list of names will be issued once all the subpoenas have been served.
The panel wants to get to the bottom of a scheme to close lanes near the George Washington Bridge, causing traffic gridlock in the town at the base of the span. The plot may have been carried out to settle a political score.