Pluck the string,(with the guitar on it's side),and let the string vibrate.
If it goes in an oval rather than side to side then it's false and needs to be replaced,(like Beandip said).
Measure the botteom of the string to the top of the first fret,If it's less than 3/32" it'll need to be raised up.If it's a bone nut you can put in a little Baking Soda and a drop of superglue.This will 'rebuild'the bone.A new nut is best,but this will work as well.
If it's a plastic nut then this could be a good excuse to put a bone,Graphtech or Tusq nut in there.