Question: God rested in the 7th day. Did He take a nap?  

Does the Bible indicate that He sleeps?

Answer: 
"Rested" = "Ceased"
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The Hebrew word translated "rested" in [Genesis 2:2](http://ref.ly/Ge2.2;nasb) is *[shabath](http://www.biblestudytools.com/lexicons/hebrew/nas/shabath.html)* (7673, שָׁבַת) literally means: to cease, desist, rest. This is the origin of the word "Sabbath," the day of rest or the day on which no work was to be done.

I posit that "rest" here means something like "at rest" (i.e. an object that is not moving) as opposed to relaxing or sleeping. He "rested" because he had (v2) "completed His work which He had done" and there was nothing left to do. He "ceased" from working because his work was finished.

It isn't sensible to think that God sleeps (as pointed out by @Mawia), nor does the text in Genesis 2:2 support such an idea.
In the Gospel of John it is written in 4:24 that God is a Spirit and spirit don't need rest or sleep. He is alive mighty God and if God sleeps then He is not a God.
According to Psalm 121 our God neither sleeps nor slumbers.