The lobbyist, AnnaMarie Knorr, has been placed on leave by the Western Growers Association, pending an investigation, the Yellow Sheet, a newsletter for Capitol insiders, reported Tuesday.
Both have told media that the relationship was platonic, although the letters suggest otherwise.
Cook, who is married, is a Republican who represents Pinal County, a rural region home to many farmers and ranchers. He sent cards and letters to Knorr that referred to her as "honey," reported the Arizona Republic, to which copies of the letters were anonymously mailed. They were signed, "Love, David oxox."
Cook sits on several committees at the Legislature that are key in farming and ranching affairs and hear bills that affect those industries, including the Land and Agriculture Committee and the Natural Resources, Energy and Water Committee.
Cook and Knorr did not immediately return voice messages seeking comment for this story.
Knorr, who apparently is also married, told the Republic that she and Cook had "never had an inappropriate relationship" and that Cook and his wife had supported her "through one of the toughest periods of my life," including while being treated for health issues.
She also told the paper that her husband, whom she had decided to divorce, and her father, Bas Aja, a powerful lobbyist for the Arizona Cattle Feeders' Association, were trying to smear her.
In one of letter the letters obtained by the Republic, Cook wrote to Knorr, "I deeply love you and on many occasions I find myself trying to protect me from being hurt by having these deep feelings for you."
Cook began writing those letters last fall, Yellow Sheet reported.
The representative initially told the newsletter that he had "no idea what you're talking about." After being confronted with the letters, he said, "All I can say is my friends, when I've needed help, have been there to help me. And I will be there to help my friends in whatever struggle they're going through."
Cook, a rancher from Globe, was elected to the Legislature in 2016 and re-elected in 2018.
In December 2018, Cook was arrested for extreme DUI. He told the DPS officer who pulled him over, "You're making a mistake," and initially handed over his ID card for the Legislature, not his driver's license.
He denied that he had been trying to demand special treatment for being a legislator, and later pleaded guilty to DUI.