The public are being asked if NHS Lanarkshire should continue to fund homoeopathic treatment at the Centre for Integrative Care, formerly known as Glasgow Homoeopathic Hospital.
A review group set up by NHS Lanarkshire has recommended cutting funding for homoeopathy at the hospital, at Gartnavel, in the West End, in 2012.
It follows a decision by NHS Highland two years ago to withdraw funding for referrals.
Chief of NHS Greater Glasgow and Clyde Robert Calderwood previously warned that if other boards follow NHS Highland, he would have to look at how much the hospital costs the board.
More than 22,000 people have signed a petition calling on the board to safeguard the hospital's future.
It is one of only four in the UK funded by the NHS and treats seriously ill patients suffering problems ranging from cancer to motor neurone disease.
Conventional medicine is combined with alternative therapies, such as acupuncture.
The three most common reasons for referral from April 1, 2012, to March 31 were rheumatoid arthritis, post-viral fatigue syndrome and multiple sclerosis.
Figures show 105 patients were referred by NHS Lanarkshire to the hospital as in- patients and 17 as day cases with 148 referred to local clinics in Lanarkshire.
A patient audit showed that around 80% of patients referred to the hospital received homoeopathy.
The health board was asked to consider the future of homoeopathy funding following a report in 2010 by the House Of Commons Science and Technology Committee, which found that remedies "perform no better than placebos, and that the principles on which homoeopathy is based are, 'scientifically implausible'.
Dr Harpreet Kohli, Director of Public Health, NHS Lanarkshire, said: "Health boards in Scotland have a responsibility to all the people they look after to provide the best quality, most effective healthcare they can.
"This means that sometimes choices have to be made between different interventions to decide which ones would be the safest, most clinically effective and cost-effective treatments to provide.
"It is right that NHS resources are used in the most effective way which may mean that some treatments which cannot be shown to work are discontinued in favour of those which do."
The public consultation will end on April 11.
Homoeopathy is based on the use of tiny amounts of highly diluted substances, which practitioners say stimulates the body to react and heal itself.
The British Medical Association previously said the NHS should stop funding such hospitals, arguing there is no evidence of their effectiveness.
Plans by NHSGGC to end inpatient services at the hospital was abandoned in 2004 after a local campaign.
To view the consultation document, visit www.nhslanarkshire.org.uk