White pushed the issue as both appeared Thursday before the Texas Association of Broadcasters.
White says Perry's handlers don't want him to have to answer questions in a debate.
Perry says White needs to reveal his tax returns from the years he was deputy energy secretary in the 1990s and suggested he may be hiding something. White has released income tax returns from his years as Houston mayor, since 2004.
White contends his finances are open to scrutiny through financial disclosure reports. He says Perry isn't as transparent as he seems by putting assets in a blind trust because they are hidden from public view.