Board member Philippa Baker-Hogan, who is also a Whanganui District councillor, said she could not agree to this.
"There are not enough benefits for the DHB. More councils have pulled out of this trial as the risks are unclear. I think we need to send a message to the council that the DHB doesn't want to be involved."
Board member Jenny Duncan, also a councillor, said she would like to know if the health board would still be liable for $21,000 if the council - and therefore the health board - decided not to go ahead with the trial.
"My understanding is that the council has committed to $50,000 of funding for the trial. If the Government goes ahead with the trial, but the council pulls out, the council is still liable to that funding. Will the DHB also be liable for its share?"
Health board chief executive Julie Patterson said she expect "all risks to be resolved" by the council.
"We should support whatever the council decides to do. It's not worth risking our partnership with the council for $21,000."
Board chairwoman Dot McKinnon said two separate voting systems would be needed if the council went ahead with the trial and the health board did not. "I would suggest that would be very costly."
All board members agreed that more information was needed before a decision could be made.
Ms Patterson was asked by board members to speak to the council's chief executive, Kym Fell, to find out what funding the health board may be liable for.
The resolution was not voted on.