Auckland Council head of parks services Mark Bowater said staff visited Totara Park first thing this morning and provided assistance to Linton.
"We worked with them to identify an individual cow being overly protective of her calf.
"During calving season, cows are typically very protective of their calves and do not like people to get near them," Bowater said.
"We recommend anyone who chooses to go in parts of our parks with cows is extra careful during calving season, as it is a cow's natural instinct to protect their calves.
"Over this time people should keep their distance from cows, and ensure they never come between them and their calves."
National RSA chief executive Jack Steer said it is always a shock to hear one "of your team being injured".
He had been in touch with a friend of Cliff's and was told he was feeling okay and not keen on a fuss being made of him and requested privacy.
"Cliff is a great guy, it's no surprise he has helped someone out when they needed it, he's just that kind of person. We wish him well for his recovery."