Labour police spokeswoman Jacinda Ardern said the fact the OIA request related also to Mr Williamson was "critical information" and it was "extraordinary" that police appeared not have mentioned this in their April 14 briefing.
Ms Tolley said it was up to police to decide "if and when an issue should be brought to my attention, and also how much information they give me".
"I back them to do the right thing and police made a decision that April 28 was the proper time to brief me."
But Ms Ardern said it was standard for ministers and staff to ask follow-up questions about OIA requests flagged by their departments.
"The question is whether or not Anne Tolley's office bothered to do that. In this case clearly they did not.
"Whilst it does seem the minister was deprived of that critical piece of information, it does seem like further down the track she took a very hands-off approach and almost a don't-ask-don't-tell stance when it came to this case relating to her colleague," Ms Ardern said.
Ms Tolley was, according to information provided by the police, the first minister they told of the email chain detailing Mr Williamsons' intervention and of their intention to release it to the Herald. However, she left it to Police Commissioner Mike Bush to tell Prime Minister John Key's department.
Ms Tolley confirmed she at no point discussed the issue directly with Mr Key or Mr Williamson.
Asked whether it was appropriate for police to have reviewed Mr Liu's case at Mr Williamson's request, she said: "Any decisions police make around the review of cases is a matter entirely for them as they are operationally independent."