It's really cute tim :)
but I'm sorry to disappoint you :( it does look like a fake -someone commented to the video's owner that it's strange that we can't see the rat's tail which is strange as rats have prominent tail that can't be just "hidden", in response he wrote:

"Hey! Don`t take it too seriously, I did not say you were stupid, you are a smart person since you are the only one who is asking about the tail, it's a humorous video, relax and smile in order to live longer"

also, Good Morning Britain host Piers Morgan said: "That's ridiculous, you've been duped by fake news", apparmtly - based upon the communication mentioned above.

source:
http://www.dailymail.co.uk/news/article-5324611/Rat-showering-like-human-bathroom-sink.html