Coughlin hit a speed of 102 mph on Sept. 18 as he rushed to a Manchester hospital with his wife.
When a trooper tried to stop them, the Coughlins called 911 and said the baby was coming. The trooper then turned the pursuit into a hospital escort.
WMUR-TV says baby Kyle was born six minutes after they reached the hospital.
The trooper congratulated Coughlin on the birth of his son and then handed him a ticket.
State Police Major Russell Conte says the trooper did the right thing, contending Coughlin put his wife, unborn child, himself and the public at risk.