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In NY state SDI or Statutory Disibility Insurance is mandatory for even one employee, with almost no exceptions. The reason is that the NY SDI is designed to cover employees for illness off the job as well as on the job.
A company may self-insure and thus avoid the SDI mandated plan, but that is more exensive because the emlpoye has to post a large bond. Self-insuring is diffent that providing a seperate short term disabiltiy insurance plan.
An employer may provide benefits under a Board approved Plan for Disability Benefits (or one negotiated by agreement and accepted by the Chair of the Board as meeting the requirements of the New York State Disability Benefits Law (DBL)(WCL §211) only when such a Plan is insured through one of the carriers licensed by New York State to write statutory disability benefits insurance policies or by an employer who has been authorized by the New York State Workers' Compensation Board to self-insure for disability benefits. All Plans accepted by the New York State Workers' Compensation Board shall cover only those employees that are eligible for benefits under the New York State DBL. Such accepted Plans must meet or exceed ALL statutory requirements as set forth by the New York State DBL.
Under such plans, SDI may be waived because it is replaced.
I would not be able to tell you definitively unless I know the character of the policy.
Let me put it simply:
1. IF the policy is approved as a self insurance plan by the state, then they do not have to also take SDI.
2. If the policy and company plan has not been accepted by the state as a self-insured plan, then they still have to also take SDI.
Since I do not know if the company's plan is accepted and approved by the state as a self insured plan, I can not tell you definitively which is true in your case.
You should be able to talk to the head of payroll or the Human Resources department and ask th em the question: is the company plan an approved self insurance plan by the state.