Yes, but sin/sit/sine decline according to the object that they describe and not the subject. So since it is "vandet", then it is "sit vand". There's a discussion about vanden vs vandet in another sentence discussion, but basically "en vand" is when talking about "en sodavand" (a soda - like Coca Cola or similar).
Sit is only used when the possession is of the subject mentioned. Assuming you're an English speaker, a good way of thinking about it is to use sit anywhere you could use "Own" in English, e.g "The cat drinks it's own water", in comparison to "It drinks its water". The second could be referring to an unmentioned other subject. Hope this helps! :)