The City Council voted 5-2 to contribute to a feasibility study for the Goodhue County History Center.
The study will examine the current building, which the city owns, and the potential to shift museum operations to the Citizens Building.
The city will contribute up to $2,450, a quarter of the study cost.
"I think this is a relatively inexpensive first step," Council member Marilyn Meinke said. "It doesn't obligate us in any way."
Council members Ralph Rauterkus and Peggy Rehder voted against the measure.
"I'm slightly concerned that we're funding a feasibility study that could potentially lead to the abandonment of a city building," Rauterkus said.
"We're not at that point," Council President Lisa Bayley said. "This is a very first step."
"In the end I think we're just losing money on this (building)," Bayley added.
Rehder said the building study shouldn't be done in isolation. For example, the old city hospital building next door to the current history center is vacant and has been for years, she noted.
"I don't think this is a well thought-out plan for a feasibility study," Rehder said. "This is striking me as patchwork."
Council Administrator Kay Kuhlmann said she will check with the architect conducting the study to see how much it would cost to examine the hospital space as well and to expand that beyond the museum.