Immigration Minister Iain Lees-Galloway said this week he was not aware of the court judgement and said it was not standard practice to have all court decisions relating to Sroubek handed to him.
Dunstan said court documents from Sroubek's run-ins with the law were provided to Lees-Galloway.
"The whole case file goes to the Minister, there is no advice provided with that and it's at the absolute discretion of that decision maker to decide."
Asked when he considered deporting Sroubek, Dunstan said Immigration NZ started preparing the deportation papers when he was on trial for using a false identity.
"He was discharged without a conviction then so that took away that automatic process."
But shortly after that he was arrested then convicted for drug dealing. His appeal on this was disallowed.
"As soon as that appeal process [is over], we started preparing the case file which went to the Minister this year."
Sroubek was in prison at the time, Dunstan said.
He added that deportation proceedings were put on hold until the legal process was concluded.
There were a number of other files the Minister received on Sroubek's case, including a "humanitarian questionnaire", as well as any information he provided which might detail the reasons why he thinks he should stay in New Zealand.
When presenting files, such as Sroubek's, to the Minister, Dunstan said Immigration NZ does not provide a deportation recommendation.
"It has to be unfettered when it goes to the decision maker and they weigh and balance that case."
However, the Minister has the opportunity to ask questions, he said.
"It's important that we don't provide advice because that could be challenged in a court."
Earlier today, the Czech Republic's Justice Ministry said it would begin the extradition process to have Sroubek sent back from New Zealand, citing outstanding criminal charges.
Asked if this information was passed onto the Minister, Dunstan would not comment.
"I don't want to go through the particulars of the case because obviously, it's under investigation at the moment."