You do not have to file a tax return for the stimulus payment if you receive SSI
See this IRS website for information - https://www.irs.gov/newsroom/va-ssi-recipients-with-eligible-children-need-to-act-by-may-5-to-quickl...
You do not need to do anything to register for a stimulus payment. The IRS will issue a payment to you the same way you get your SSI payments. You can track the status using the IRS portal: Get My Payment | Internal Revenue Service
See the answer from DoninGA above if you have dependents under age 17 that you need to add to get the $500 payment for them.
so don't. the IRS says that SSI recipients who use direct deposit will get the stimukus directly deposited into the same account. however, the iRS needs to update its database to do this and I know quite a few SSI'er that haven't gotten it yet. if you don't use direct deposit the IRS will send you a check.