Is there a relationship between asperger and dysgraphia?

No: Dysgraphia, which simply means bad handwriting, is completely different from and unrelated to asperger's disorder or autism.

Motor clumsiness in: Kids with aspergers often manifests as robotic walking, lacking normal arm swing. It can include deficits in manual dexterity. Executive function deficits including poor motor planning are seen in as +/- adhd some with as have non-verbal learning disabilities. Poor visual-spatial processing & propriokinesthestic sense, "feeling" where one's body parts are, can cause dysgraphia; hypotonia also.

If they have low : Muscle tone ( low resistance to passive movement) with delayed fine motor skills, for which they require occupational therapy, they later have abnormal pencil grips & dysgraphia. On neurodevelopmental exam, finger agnosia (not being able to mimic touching the correct finger to their thumb " by feel" indicates a deficit in proprioceptive-kinesthetic sense. This is not specific to autistic disorder.