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

Does the Bible indicate that He sleeps?

Answer: 
No! God doesn't sleep nor needs to sleep. God is not a human.

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> Indeed, he who watches over Israel will neither slumber nor sleep. (Psalm 121:4, NIV)
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I would mock and laugh at any god who needs to sleep. A god who needs to sleep is not a true God at all. The idea that God would sleep was humorous to Elijah the prophet.

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> 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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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.