In September, the regulator pledged to carry out a review of its approach to registering such organisations after the charity the Good Thinking Society called on it to revoke the charitable status of organisations that promoted what the society called "disproven treatments", including homeopathic remedies and those that discouraged vaccination or promote "energy healing".
The society threatened to take legal action against the commission if it did not do so.
In its statement announcing the consultation yesterday, the regulator said it did not support or oppose CAM therapies and that registration of organisations promoting them was not an endorsement.
"Instead, registration requires a legal test, in which the commission considers a number of factors, including whether an organisation’s purposes are beneficial to the public and whether any potential harm may outweigh the benefits," it said.
The statement said this area of policy had not been reviewed for some time and the commission wanted to ensure its approach reflected the current state of the law and the available evidence about CAM therapies.
The consultation asks what level and nature of evidence the commission should require to establish the beneficial impact of CAM therapies and how it should consider conflicting or inconsistent evidence of the impact of them.
It also asks whether the commission should distinguish between organisations that promote CAM therapies as accompaniments to conventional medicine and those that say it should be a replacement, and whether it should ask for a lower level of evidence for therapies that are purported to relieve symptoms rather than to cure or diagnose conditions.
John Maton, head of charitable status at the commission, said: "The commission has the task of deciding which organisations are charities, but we recognise that we are not the authority in the efficacy of non-traditional medical treatments.
"Our consultation is not about whether complementary and alternative therapies and medicines are ‘good’ or ‘bad’, but about what level of evidence we should require when making assessments about an organisation’s charitable status. This is an area of considerable debate and it is important that we consult openly."
He said the commission would also engage with key stakeholders and hold focused discussions with relevant organisations as part of the consultation.
The consultation will close at midnight on 19 May.