A state trooper in Oregon made a “very rare and unusual” find last week — two deer still alive despite arrows protruding from their bodies, including one to the head, authorities said.

Oregon State Police said a trooper responded to the Shady Cove area in Jackson County on Friday after receiving a report that a deer had been shot with an arrow that was still stuck in the animal. After an initial unsuccessful search, a trooper responded later Friday and found two deer with arrows sticking out of their bodies.

The injuries did not appear to be life-threatening, but officials now hope to track down and capture the animals to remove the arrows, according to Oregon State Police Sgt. Kaito Raiser.

“I have not heard of a situation like this in the past, so this is very rare and unusual,” Raiser told The Post in an email, adding that the animals had not been located as of midday Monday.

Investigators believe there also may be a third deer in the area with an arrow stuck in its body. Troopers must get about 30 yards away from the animals for them to be tranquilized and captured, which is “difficult to due wild game,” Raiser wrote.

No suspects have been identified as of early Monday and a $2,000 reward is being offered for information leading to an arrest in the case, which could lead to charges of cruelty to animals. The deer were also shot outside of season with arrows typically not used for hunting, Raiser said.

“These arrows are not hunting-style arrows, and they’re really intended to act like a gunshot to travel through the animal and create the most damage possible,” Raiser told The Post during a brief telephone interview. “And a legitimate hunter would never intentionally target those area of a deer to take the animal. Those are not areas of the animal that are commonly targeted.”

The deer, meanwhile, appeared to be in fairly good shape considering they were targeted intentionally, Raiser said.

“Considering the situation, they’re still able to get around and survive at this point,” he said. “How long that will last, I wouldn’t be able to speculate.”

Anyone with information about the animals is asked to contact the Oregon Hunters Association’s Turn-in-Poachers program at (800) 452-7888.