It took a week after the discovery of the house for the council to be told where it was, and director of planning and environment Chris Berry expressed frustration at the delay – and at the fact that he had first heard of the discovery through the media.

But he was finally given the address on Wednesday. It was a rural property between Murrumbateman and the Canberra border and he believed it was owner occupied, he said.

To date, 77 owners in the Yass have asked to have their homes tested for the loose-fill asbestos, which is assumed to pose a much bigger risk in NSW homes because it remains in ceilings, having never been cleared out as it was in Canberra 20 years ago.

Thirty-seven Yass homes have been tested and 36 of those cleared. The new discovery brings to two the number of Fluffy homes in the Yass council area, with another home on a farm block not far from Canberra already known to have been part of the Fluffy cohort.

Mr Berry said the home would be listed on internal council records so any buyers would be told and in case of an application to extend or demolish. Council offers also needed to know in case they visited the home.

"It's a bit annoying ... that the first house that comes along and get identified in this process we're the last to know," Mr Berry said before being told the address late in the day.

"My concern at our end is what happens if we get a building application? We need to know that information so we can make appropriate decisions, otherwise we could issue a building approval not knowing it's a Mr Fluffy house, the tradie picks it up and goes and does his extension and all of a sudden he's exposed."

A spokesman for the NSW taskforce said the Yass council had been told of the discovery of a home in its area by phone and in writing on the day of the discovery, but the address could only be released to the council after owners gave their signed consent.

He said it was up to councils whether to list Fluffy properties on their S149 certificates, notifying buyers if it was on the market.

Mr Berry has encouraged Yass owners to put their hands up for the free testing, offered till August this year, but acknowledges that people who suspect they have Fluffy insulation in their ceilings might be reluctant to do so because of the uncertainty surrounding what will happen to their home.

NSW Finance Minister Dominic Perrottet has set up a taskforce, to report by the end of May on the most cost-effective option to buy back and demolish the houses, and has acknowledged that demolition is the only enduring solution.