McKenna, the state's attorney general, said he has disclosed enough information in the personal financial forms that candidates file with the state. He called the tax-return debate - both here and nationally - a "phony issue."
McKenna, a Republican, said his political rivals are attempting "to change the subject away from the real issues of the state."
Democratic rival Jay Inslee, a former congressman, released five years of tax returns last week, and his campaign had called on McKenna to do the same.
McKenna noted that the matter follows closely with what is happening in politics nationally. President Barack Obama has been calling on Republican presidential candidate Mitt Romney to release more of his tax returns. Romney has declined.
McKenna said he didn't want to be dragged into a game.
The personal financial disclosures that McKenna files in Washington do provide some detailed information, such as donations from groups that have covered costs during McKenna speaking engagements. But some of the numbers can be vague, as the forms provide only broad estimates for income from investments.
Tax returns would also provide more specific detail on household income, how much the family paid in taxes, any types of exemptions the family claimed and how much the McKennas gave in charitable contributions.
McKenna and Inslee are set to meet Wednesday night for their second debate. The event will be hosted at Washington State University's campus in Vancouver.