If a participant chooses to receive disability benefits on an after-tax basis, can pre-tax deductions such as health care premiums be withheld from the disability payment? Or can pre-tax deductions only be taken from pre-tax disability payments?

If the disability payments are part of a Salary Continuation Plan the I say yes.

If the disability payments are from the insurance company and therefore not on the payroll, the answer is No.

If the disabilty payments are on account of the personal physical injury or illness and not for the time absent from work, the answer is No.

Pre tax deductions are really Salary Reductions and therefore must come through a payroll paying wages, salary or employee compensation for services (with a few exceptions).

Agreed. If the disability payments are going to the disabled directly from the insurer, there's no way to make deductions.

If you are looking to offer the benefit of pre-tax deductions for medical insurance, change your disability plan to a salary reimbursement plan. This way the checks from the insurer will come directly to you and you reimburse the employee through payroll. I would only do this for short-term disability, however, since you only have an obligation for 13, 26 or 52 weeks at most.