Mr Bezett said he was unwilling to discuss the matter.
"He's got a particular attitude that's hopefully being sorted out," Mr Bezett said.
"He's threatened to go to the media a number of times, he's gone to the mayor, he's gone to police and most people have ignored him," he said.
Mr Hawkins said: "It's absolutely astounding that a councillor would stoop to this level."
The dispute related to access to a right-of-way on Mr Bezett's property.
The Hawkins say the easement is their legal right, the neighbours do not share the driveway and Mr Bezett is blocking their vehicles in.
The couple cannot park their vehicles at the top of the driveway because it is unstable owing to storm water and Mr Bezett took umbrage to their parking further down, Mr Hawkins said.
However, both parties could use the driveway if they were being accommodating, he said.
Senior Sergeant Brian Benn said police received a complaint from Mr Hawkins yesterday.
While the matter was a civil dispute, police would follow with both parties today, he said.
Mr Hawkins said he believed Mr Bezett was using his council position to bully them.
Last Friday, Mr Bezett parked his car in the driveway so the Hawkins could not get their cars out and then used his bicycle to ride to work, Mr Hawkins said.
He called a towing company to remove the vehicle, but said the company refused.
"We were absolutely gobsmacked - we couldn't believe he would just lock his car and get on his push bike and leave his car there for the day," Mr Hawkins said.
Mr Bezett rang him during the weekend.
Mr Hawkins played a recording of that conversation to the Otago Daily Times and after a brief exchange, Mr Bezett can be heard saying: "You'd best be prepared to catch the bus in the morning."
Mr Hawkins said he had previously maintained good relations with the councillor and had allowed him to landscape an area of the couple's frontage into his yard under a "gentleman's agreement".
"We were at one stage talking about moving the boundary to accommodate him and that's not going to happen now."