A complete search of the internet has found these results:
I laid down is the most popular phrase on the web.
Both "laid down" and "layed down" mean the speaker set something down. They are two different spellings of the same past-tense verb.
843,001 results on the web
That day when I laid down to rest, I was dead tired.
I laid down for a short nap and fell asleep for two hours.
He laid down can keep them awake for now, although they might take a nap later.
You may even wake up feeling worse than when you laid down.
You laid down right in front of my and asked me for some of my food!
I laid down and died that night.
She laid down on the bed and fell instantly to sleep.
403,994 results on the web
He layed down his hammer and a little piece of steel.
She layed down her one-month-old baby in the bassinet.
They layed down their lives for their jobs.
You layed down the new carpet today, right?
Did she say that she layed down the tiles in the bathroom already?
She layed down the sod around the perimeter of the house.
Did you already lay down the new carpet, dear?
I layed down the law when I was the sheriff of that small town.