Technically the answer is "I am not she," according to traditional English grammar. It's an example of what's called a "predicate nominative," and it (traditionally) works the same way in English as in Russian (among other languages): when you use the verb "is" to show that two things are identical ("I am she"), both the subject and the predicate take the nominative case.
The truth is, though, that nobody ever says this anymore, and many native speakers will think it's incorrect if they hear it. This is because in English, pronouns are the only words that even have cases, and although we use "is" all the time, it's rare for us to use "is" with pronouns, because it's rare to talk about one person being (or not being) identical to another person. We're used to always hearing pronouns in the accusative when they follow a verb, and so we expect to hear the accusative forms of pronouns (me, him, her) after the verb "is," too.
At this point, based on standard usage, it's more correct to say "She's not me." You may find grammar books that will claim otherwise, but even in formal writing, very few people will actually use the traditionally "correct" form anymore. (However, in rare cases you may still hear a phone conversation, usually with an older person, that goes like this: "Hello?" "Hello, I'm calling for Mary." "This is she.")