A 56-year-old man was arrested on suspicion of drink-driving, driving without a licence or insurance, and assaulting a police officer following the incident in Great North Road, Gamston, near Tuxford.
Another man who was also in the car was being arrested when he ran off.
Officers later arrested a 57-year-old man on suspicion of evading police custody.
Sergeant Howard Kirkland, of Nottinghamshire Police, said: "Assaults on police officers are totally unacceptable.
"Officers are members of the community like anyone else, who have family members and colleagues who are concerned for their wellbeing.
"They pull on the uniform each day to do an extraordinary public service to keep the people of Nottinghamshire safe, so it is always saddening to hear when they are hurt while doing that.
"Any assaults on emergency workers are treated very seriously and we will always look to put people before the courts as soon as we can if they are suspected of offences like this."