Can osteopathic doctors perform upper cervical manipulation like chiropractors do?

OMT. Osteopathic physicians who perform omt can do so for cervical, thoracic and lumbar region pain. They can also prescribe any medications appropriate to assist with your recovery. It all depends on their level of training and expertise.
Yes. Yes, most certainly they can and often it is more precise and gentle in technique but it depends on the training and experience of the D.O.
Yes. Actually their training is world's better than chiropractors. Osteopaths can make proper diagnoses, prescribe effective treatment and perform manipulation in a safe and effective manner. Never, never let a chiropractor touch your neck - it is dangerous in the extreme.