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Hi, I can help you with your question today.
Other than sitting in the bowl of water, what other behaviors are you seeing?
It's certainly not typical, but some cats actually do like water.
I'm concerned about a couple different things from your description. She may have fleas - the water would be soothing and enough fleas can cause anemia in a young kitten. Also, if her behavior is off, this could indicate a neurologic problem. Since she has no known vaccine history, neurologic disease could be caused by rabies virus.
If you could ensure that you will not get bitten, it would be best to have this little one examined by a local vet. You can try to entice her into a carrier with some canned food or tuna placed in the back of the crate or carrier, then close the door once she's inside.
I'm so sorry. If you touched the kitten, I highly recommend that you contact animal control. The kitten's signs and death are suspicious for rabies, and if there is any chance you were exposed they will need to test the kitten.