O'Toole did not immediately return a call Monday. A legislative aide said he was with clients. The Newark Star-Ledger, which first reported the allegations, said he denied them.
Codey, Gill, and Sen. Ronald Rice, all Democrats representing Essex County, signed the letter last month to state Supreme Court Justice Stuart Rabner.
But Codey says it was Gill who heard the allegations from people involved.
Gill declined an interview request Monday, instead offering a one-sentence comment through a spokeswoman: "We are going to let the chief justice handle the matter."
Gill had been blocking Dow's nomination as part of a standoff with Gov. Christie over nominations.
Codey said that O'Toole approached Costello in May with the request to pressure two subordinates. Costello's office referred all calls to state judiciary spokeswoman Winnie Comfort, who would only confirm that Rabner had received the letter.
Codey said that the senators contacted Rabner because they believe that if O'Toole's acted in that manner, it would violate rules of professional conduct for lawyers.
If the allegations are true, the threats were not followed through. Gill never agreed to support Dow's nomination in Essex County.
In late May, Christie withdrew his nomination of Dow to the bench in Essex County and instead nominated her to a judgeship in Burlington County. He also renominated both Siobhan Teare and Verna Leath, the Essex County judges whose nominations were in question. The senators do not allege that either of those judges tried to lobby Gill - just that they were asked to do so.
Christie's spokesman Michael Drewniak said in an e-mail that given all that, the allegations are not credible.
"From where we sit, this makes no sense at all given the actual events," he said.