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It follows a report in February from Invercargill City Council chief executive Clare Hadley who confirmed council ownership.
At the time, the board was surprised and requested evidence.
Ms Hadley referred to minutes and press articles proving council’s ownership.
While board member Roger Eagles accepted historical factors, he said the document did not have much legal weight.
"Ms Hadley may be correct or she may not. It is difficult to know ... I think it should be the subject of a proper legal opinion.
"But at the end of all this the board needs to consider what it should do now. It could just let the whole matter lie because the building or collection of buildings is probably [more of] a liability than an asset now.
"We will not be able to do anything with the building ourselves. The building will probably be demolished and a new building will be created."
Southland Mayor Gary Tong said if it sought legal advice the board would be "broke".
Museum board member Evelyn Cook agreed.
"I don’t want to see us investing more money and time in chasing this particular rabbit down the hole. I think whatever we have contributed as a board financially ... is irrelevant now. The complex as it is is not fit any more for purpose."
Christine Henderson said ownership at this point was a "moot point".
The board accepted council’s ownership and said they would focus on repurposing SMAG Trust Board after a proposal to transfer the governance and management of the Southland Museum and Art Gallery to the Invercargill City Council had been endorsed by all funding councils.