Close to 90% of Neandethals were right-handed. Much of this data comes from comparing the muscularity of their arms, which show clear differences. However, arms aren’t the only way you can tell a lefty from a righty. You can also look at that individual’s teeth.
How often have you used your teeth as a tool to hold, pull or tear something? Neanderthals, with their much stronger jaws, presumably made even more use of their teeth. Wear patterns on their enamel confirm this. A right-handed person who routinely uses his mouth as a vise grip will not wear down the same sides of his teeth as a left-handed person. You can try this yourself (though hopefully not to the point of damaging your enamel). Thus, by looking at the scratches on fossilized teeth, you can tell whether that individual was right or left-handed.
Virginie Volpato of the Senckenberg Research Institute Frankfurt and her colleagues examined the teeth and skeleton of one particular Neanderthal specimen (Regourdou 1). They found that using his teeth to determine his handedness yielded the same result as using his arm asymmetry. This strengthens the idea that you can distinguish right from left-handed Neanderthals and also confirms that most of them were in fact righties.
Labial scratches on Regourdou 1’s anterior teeth.
Virginie Volpato, Roberto Macchiarelli, Debbie Guatelli-Steinberg, Ivana Fiore, Luca Bondioli, & David W. Frayer (2012). Hand to Mouth in a Neandertal: Right-Handedness in Regourdou 1 PLoS ONE DOI: 10.1371/journal.pone.0043949.g004