As per TurboTax
Temporary disability, such as an injury, serious medical condition, or even pregnancy, short-term disability payments can be obtained through private insurers, and they may be part of an employer’s compensation to employees. Whether the payments are taxable depends on how and when they are paid.
Employer disability benefits
If you and your employer share the cost of a disability plan, you are
only liable for taxes on the amount received due to payments made by
your employer. So, if you pay the entire cost of a sickness or injury
plan with after-tax money, you do not need to report any payments you
receive under the plan as income. If your employer pays half the cost
of premiums and does not deduct these payments from your pay, then you
most likely must report half the payments received as income.
Reimbursement of medical costs you’ve paid for after the plan was
established are not taxable, but may reduce the amount of your medical
costs deduction.
As per IRS
Finally, the applicable statutes and regulations do not distinguish
between short-term and long-term disability plans. Thus, if an
employer offers both short-term and long-term disability plans and
permits employees to separately elect the contribution payment method
for each plan, the law does not require aggregation of the
contributions paid for each plan in determining the taxation of
benefits. Benefits paid under a short-term or long-term disability
plan will be taxed according to the contribution payment election made
for each type of coverage.