Mrs King told about 30 people at a public meeting in the resort last night a mooted community trust model had a mixed record around the country.
A community-owned hospital was unlikely to receive government funding for upgrades and maintenance, the costs of which could swamp a small population.
''I don't think the people of Queenstown should accept that.
''It's a public facility - what you need to fight for is your fair share of funding and what needs to be provided here.
''Don't blame the Southern DHB. Go to the Government and demand it.
''There's some real risks in becoming a trust, even if [the hospital] is handed over for a dollar.''
But if the community decided to take over the hospital, it first needed to find out what it would be liable for: ''I wouldn't make a move until I got answers to all those questions.''
An Australasian consultancy firm is expected to present a report to the Ministry of Health later this month advising how the hospital could be removed from Southern DHB control.
Mrs King, who was accompanied to the Grey Power-organised meeting by Dunedin North Labour MP David Clark, said they had been visiting rural hospitals in the lower South Island and could ''see the impact of cuts to rural health''.
The population-based formula for funding DHBs was not meeting the region's needs, and urgently needed to be reviewed.
The pair will visit Lakes District Hospital today.
