Muon spin resonance (mu SR) is a powerful technique for investigating the local magnetic fields in materials through implanted muons. Here we report a mu SR study of chemically produced thermally exfoliated graphene. Our results provide an experimental answer to the many theoretical investigations of magnetic properties of graphene. The observed muon spin precession is attributed to a localized muon-hydrogen nuclear dipolar interaction rather than to a hyperfine interaction with magnetic electrons. This proves the absence of magnetism in chemically produced thermally exfoliated graphene.