Stating a post doc research fellowship that I declined on my CV due to personal reasons?
I don't think there is a clear answer to this that would apply in all situations. There are both positive and negative aspects to it. Yes, you were awarded a nice position. Yes, you backed out. For some situations one or the other of these might be more important. 

I'd suggest that for purposes of applying to a position you evaluate the situation and send a CV tailored to their needs. It may, in general, be safer to omit it if you think it might raise any questions. You can always bring it up in an interview later if you think it might be worth it. 

But most employers will want some assurance that backing out isn't a habit. So, for a general CV visible to the masses, maybe a bit better to omit it.