Boochani had indicated he would consider seeking asylum in New Zealand but under this country's law ministers and officials cannot discuss any details of individual claims or even confirm if an application has been made.
Under immigration law, someone seeking asylum can be granted a temporary visa so they can live and work in New Zealand while their application is being considered, a process that can take several months.
National's immigration spokesman, Stuart Smith, said National is questioning whether Boochani truly intended to leave New Zealand after a month, as he would have been required to state on his visitor visa application.
When applying for a visa people had to show they were a "genuine tourist or visitor", said Smith, and state their intention to leave.
In an interview with ABC before he arrived in New Zealand, Smith said Boochani indicated he had "no intention of leaving New Zealand" once his visitor visa expired.
There was no justification for using a visitor visa to get to New Zealand in order to then seek asylum, Smith said.
"He had been accepted for asylum in the US, so it's not like a normal case of someone claiming asylum when they get in the country that has nowhere else to go - quite clearly he did."
There was a "bad odour" around the whole application process, Smith said, "but what's happened since we don't know and we won't know possibly at all.
"His legal status once he's here is quite tightly defined and that may be a difficult situation but this man got into New Zealand when he quite clearly stated he was considering not leaving the country ... the wrong way to go about filling out your visa form."
Prime Minister Jacinda Ardern today told Morning Report that by law she was not able to comment on an individual's legal status or applications.
"Generally, of course, we have an expectation that people, when they are in New Zealand, are here legally and Immigration takes action if they are not."
In November Ardern said she would have preferred Immigration Minister Iain Lees-Galloway to have given her a "heads-up" about Boochani's arrival, adding, "It is still a matter that, ultimately, would not have changed as a result of me knowing."
"It was an operational decision, though, made by Immigration New Zealand, as you would expect for a visa decision."
When asked about statements Boochani had made about maybe staying on past his visa, Ardern said at that time it was "totally hypothetical".
"He has the legal ability to be here for a month. It demonstrates, I think, the system where he's been identified already as a refugee - he has travel documents and he's had the ability to apply and legally be here in New Zealand for the purposes of speaking at a conference," Ardern told reporters.
"He also, of course, is in the process of gaining approval to be able to reside in the United States. Anything beyond that really is, you know, speculative."
Asylum claims in New Zealand were dealt with "totally independently of politicians", she said.
In a statement, Lees-Galloway said he could neither "confirm nor deny whether Immigration New Zealand had received any claim for asylum" under the section of the Immigration Act that "requires us to keep all refugee and protection claims confidential".
"Asylum claims are very sensitive in nature and are often made because the individual has a fear of persecution in their country or otherwise fear to return there.
"As such, it is important that the existence of any claim is kept confidential to protect the individual while their claim is being assessed."
Boochani has not responded to a request for comment from RNZ.
