There are many ways to find this information out. On your own and for free, you can search http://a836-acris.nyc.gov/CP/ for the public records involving the ownership of the subject property. You can also contact and pay a title company for a correct and up to date chain of title, or you can retain an attorney to do the same.
Get a title report to track ownership and possibly consult with a probate attorney to determine if you inherited an interest in this property.
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As my colleague indicates, you can search the New York City ACRIS (online property records) system. However, that may only go back to the 1970s. If your grandmother purchased prior to that, you could go to county recorder's office with the street address and they will help you find the last deed for the property. Alternately, you may hire a title company to provide you with an abstract of title.
If your grandmother intended to leave you the property, that information would likely be found in her Last Will.
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If the property was indeed within NYC and the ACRIS search reflects that the property is still in your grandmother's name, then you should seriously consider consulting with an estate attorney, for the purposes of possibly petitioning the Surrogate Court, to administer her estate, including the property.
Please be advised that this answer shall not constitute legal advice, or create an attorney-client relationship.