What Are The Symptoms Of Cerebral Palsy?

My 6 months old seems like a happy, healthy, baby. He eats well, rolls over, coos, laughs, smiles, and loves to be talked to but he's always been abnormally stiff to me. At first I thought it was normal but the more I look into it the less normal it seems. He isn't sitting up yet and although he moves all his limbs equally he does have his fist close quiet a bit. I keep reading about cerebral palsy and I fear that my son might have this. He had a normal birth and was born at almost 38 weeks. I know there's no way to diagnose someone with cp without several test but my question is can my child just have hypertonicity and not have cp?