While CRTs could emit X rays, LCDs don't. But there are a few that are sensitive to even the slightest of EM so you must be gentle with them and hope they'll ask their doctors.
Frankly, the worry is up to you as there is no X ray radiation source in laptops.
i bought a brand new HP mini notebook around a year ago and i've had it hooked to the AC supply permanently and have been using it for long periods of time that exceeds 7 hours per day, just like when one would use a desktop.
frankly i've never had a desktop in my life except from years ago and i've always borrowed my friend's pc since i'm crashing in his place, but ever since i got my laptop i've been sitting infront of it for many hours everyday and i've been doing this for 4 months, so i'm wondering if i've been exposed to large amounts of laptop radiation since laptops are only supposed to be powered on for 4 hours until the battery dies out, but now i basically had it on 24/7 on hard power supply on the dinner table and uses it for long durations just like a desktop without those professional laptop shield.
granted i didn't put it in my lap and i just sat with the laptop on the table proper so no worries about my genitals being affected and i always made sure the laptop itself is always half an arm's length away from me but i'm still worried about getting cancer sooner because after googling for awhile it seems laptop radiations don't always meet safety standards, maybe its time i get a proper desktop for good. well share your thoughts with me i'd like to know what you folks think, chao!