And only one in three patients who requested a cannabis prescription were successful.
Medicinal cannabis users said barriers included price and the limited range of cannabis-based products available on prescription.
However, many respondents also explained they were reluctant to ask for a prescription due to the fear of being judged, researchers said.
The paper said this was in line with other recent New Zealand research where about two out of three surveyed GPs did not prescribe a cannabis-based product at the time of patient request.
Under the planned reforms there is currently no list of eligible conditions and the decision about prescribing was left to treating clinicians, researchers said.
Despite the limited engagement of medicinal cannabis users with the current legal access route, most respondents indicated their willingness to engage with the new Medicinal Cannabis Scheme (MCS).
Researchers said the legalisation of cannabis for recreational use, pending results of the September 2020 referendum, may also provide an alternative way of supply, with the convenience of price and access but at the expense of medical oversight.
"A challenge in studying medicinal cannabis use lies in the blurred boundary between medical, therapeutic and recreational uses of cannabis.
"Like other studies, including previous analysis of New Zealand Health Survey data, we found a significant proportion of medicinal cannabis users also use cannabis recreationally," the paper said.
Meanwhile, another study published in the NZMJ revealed varied attitudes among middle-aged New Zealanders on cannabis and the proposed law change.
At age 40, 899 participants drawn from the Christchurch Health and Development Study were interviewed about the perceived harmfulness of cannabis use, opinions on legalisation for recreational use and supply, and the use of cannabis for medicinal purposes.
Researchers were careful to note that the data was collected in June 2017 and June 2019, meaning that most interviews were conducted before the announcement of the referendum on the Cannabis Legalisation and Control Bill in New Zealand in 2020.
Overall, the research showed attitudes towards cannabis use and the law change varied widely, but the majority (80 per cent) supported use for medicinal purposes.
The number of people in support of decriminalisation was considerably less (47.8 per cent) and an even smaller amount (26.8 per cent) expressed support for legalisation for recreational use.
Those with longer durations of drug use, and particularly cannabis use, tended to hold the most positive views towards cannabis use and legalisation.
By ethnicity, Māori tended to be more in favour of the law change and researchers argued that was because Māori had a higher rate of use and were at greater risk of being arrested or convicted of a cannabis-related offence.
The legislation on cannabis has already passed and when New Zealanders vote "yes" or "no" on September 19 it will be binding.
The referendum to legalise personal use of cannabis, on the other hand, is not officially binding. But both the Coalition Government and the opposition National Party have said they will honour what the majority votes for.
The Cannabis Legislation and Control Bill would make it legal to use or grow cannabis for recreational purposes in New Zealand.
The production, supply and use of cannabis would be regulated by a new Government-controlled authority.
To read about the cannabis referendum click here
