If you do have your school tax bill receipt, and it shows a reduction in school tax due to STAR, then you probably didn't receive a check. However, you may have received a check for credit for property tax relief or property tax freeze.
Last year I had a question about a check that was sent to me so I called the NY State Dept of Taxation & Finance, and they were able to look up the amounts they sent me and the dates they were sent.
Here is the contact info page: https://www.tax.ny.gov/help/contact/#phonenumbers
The web site says they are experiencing high call volumes, so be prepared to be on hold for a while.
