Nope, you just need to have the cash needed to cover the cover the value of the put if sold. Reference "cash secured puts"
I know this...and everyone else should know it too. But my post was answering the the post before that said there was a need for Shorting if you had Puts. But there is no need to have Shorting in order to buy/sell Puts. Shorting has nothing to do with Shorting.