They're both correct. With some words, such as study, work, live, the choice of aspect makes little difference. The meanings are similar, however I recommend you use I am studying, to emphasize the fact that it's just temporary -- someday you will finish your studies and do something else.

Where do you study ... I study in gov school, is correct

As Phil says, you could use either of this tenses. The present continuous suggests a temporary situation, while the presents simple suggest a more permanent one, but in fact either form is be appropriate here. But can I just point out an equally important grammar point about your studies? You need to say: 'I am a law student'. This is a compound noun made up of two nouns, one after the other. The second, more general, noun tells us what you are - a student. The first, more specific, noun tells us what kind of student you are - a law student. There is no possession involved here, so it is not possible to use a genitive 's' form. You don't belong to the law, so you can't say 'law's' student any more than you can say 'an English's teacher'. This is an extremely common misunderstanding among Italian learners, and I really wish that more teachers taught this to their Italian students!

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