Short answer: It depends on who paid the premiums. If your employer paid, or you paid through a pre-tax plan, the benefits are taxable; if you paid the full premium with after-tax dollars, they are tax-free.
The IRS decides whether disability benefits are taxable based on whether the premiums were taxed first. Employer-paid premiums that were not included in your income mean the benefits are taxable when you collect them. The same result applies if you paid your share through a cafeteria plan with pre-tax dollars, because those premiums are then treated as paid by your employer.
If you paid the entire premium yourself with after-tax money, you can exclude the benefits from income. If you and your employer split the cost and your share was after-tax, only the part of the benefit attributable to the employer’s payments is taxable. This is why some employees choose to pay disability premiums on an after-tax basis: it makes any future benefit tax-free. Short-term and long-term disability coverage follow the same rule.