The attacks took place in the Baltic Sea, a small town near the Rhode Island state line. The golfer was injured at the golf course of Mohegan Sun and the horse at a house nearby.
The golfer was near the seventh hole in the late 1960s when he was attacked.
Another member of the golfer team was able to drive out the Bobcat and the attacked golfer was sent to a trauma treatment hospital. His condition is unknown. Bobcats are common in Connecticut, but are usually shy, secret animals.
Attacks on humans are extremely rare, according to the Department of Energy and Environmental Protection.
Before the attack on the golf course, Loree Osowski's horse was attacked by a bobcat, suffering from both neck and eye treated by a veterinarian.
The Bobcat finally ran away and called 911. Her horse received 16 stitches and some booster shots to be good.
"In my 20 years with the DEEP, I only had three rabid boobies," said Dwyer. "They are extremely aggressive and extremely vicious if they have the rabies virus, I'm not saying it, but it's being tested, this time these incidents are usually associated with a sick animal."
In Connecticut, the last reported incident ended 8 miles from the Baltic Sea in August 2014.
Rebekah Riess and Jessica Prater of CNN contributed to this report.