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

Does the Bible indicate that He sleeps?

Answer: 
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.
Just to add to previous answers.

For clarity, Sleep is a physiological phenomenon,

"characterized by altered consciousness, relatively inhibited sensory activity, inhibition of nearly all voluntary muscles, and reduced interactions with surroundings." - <https://en.wikipedia.org/wiki/Sleep>

While it's a subject of ongoing research, sleep is generally associated with the need to rest, with being tired, a direct association with being material and mortal.

As stated, God is not human, He is immaterial and eternal (Revelation 1:8, John 4:24). The idea of God sleeping doesn't make sense. Similar to asking if a bachelor can be married.

The example given above with Elijah: 

> 
> At noon Elijah began to make fun of them. “Pray louder!” he said. “If Baal really is a god, maybe he is thinking, or busy, or traveling! Maybe he is sleeping so you will have to wake him!” (1 Kings 18:27, NCV)
> 
> 
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Elijah is not just making fun of his opponents god's failure to act. He is, in a sense, charging them with not being real god's (or not even being real at all!).