Welcome to the Q&A Forum
Browse the forum for helpful insights and fresh discussions about all things SEO.
After more than 13 years, and tens of thousands of questions, Moz Q&A closed on 12th December 2024. Whilst we’re not completely removing the content - many posts will still be possible to view - we have locked both new posts and new replies. More details here.
My first thought is "No, you shouldn't".
First of all, nofollow is a tool to stop other websites from getting link juice. This is primary for websites you don't trust. But I believe you trust Youtube, right? 
Plus that it's your own videos on Youtube that you link to, another reason to not put nofollow.