The board voted on Thursday to include up to $30,000 in the 2020-21 annual plan to allow for preliminary design and cost estimates for the two buildings.
Central Otago District Council property and facilities officer Tara Bates said both buildings were listed as civil defence centres in the community emergency response plan.
This meant they were considered priority buildings and would need a higher degree of strengthening.
Millers Flat Hall was given an initial assessment in 2013 which placed the hall at about 37% of new building standard (NBS).
Roxburgh Entertainment Centre was strengthened in 2017 to 34% NBS, she said.
Both buildings would need to be at about 67% NBS or higher if they were to continue as priority buildings in the emergency response plan.
The decision to designate Millers Flat Hall as a civil defence centre was ultimately a decision for the community board, he said.
"That is why we have such a close consultation with the community and the community board," he said.
The board voted for discretion to close a council-owned earthquake-prone building be with the Central Otago District Council not with the board, as part of district risk management.
Teviot Valley Community Board chairman Raymond Gunn said they were talking "big dollars" if earthquake-strengthening including steel framing was needed for the entertainment centre.
