You can't electrolyze urea by solving it in water and passing electricity through the solution, for that you'd have to melt pure urea and electrolyze that. Problem is that it will decompose above its melting point.

So, even when urea is solved in the water, only the water is electrolyzed (in hydrogen and oxygen).

Why would you need to melt the urea to electrolyze it? I'm actually a little behind with my chemistry, but you can electrolyze NaCl (salt) when dissolved in water, without melting it. The basic requirement is that the solution contains ions. Now I must admit that I don't know the basic reactions of urea with water, but given that you can use urea as hydrogen source in fuel cells [1] I'd assume that it should work as hydrogen source in an electrolytic process since the basic reaction is somewhat similar.

[1] see https://en.wikipedia.org/wiki/Urea#Laboratory_uses

Edit: There are papers about direct electrolysis of urea

http://www.suttonfruit.com/pics/urea_electrolysis.pdf (I think its a copy of http://pubs.rsc.org/en/Content/ArticleLanding/2009/CC/b90597...)

http://etd.ohiolink.edu/send-pdf.cgi/Singh%20Deepika.pdf?ohi...

Now I don't know how legit they are, but seems ok to me.