Carr, a sophomore from The Woodlands, Texas, completed CU's summer school session on Friday and asked for a transfer.
"Patrick is a fine young man who needs to move closer to home back in Texas for family reasons," CU head coach Mike MacIntyre said in a quote provided by CU. "We enjoyed having him in the program and wish him and his family the best."
As a true freshman last season, Carr was fourth on the team with 272 rushing yards on 66 carries. He had his best game in a 35-31 loss at UCLA, when he ran for 100 yards and his only touchdown on 19 carries. On the season, he also caught five passes for 52 yards.
During spring drills, Carr was praised several times by coaches for his performance in practice and for the way he was grasping the offense. Since Carr's arrival last year, CU coaches have loved his speed and big-play potential.
In addition to football, Carr participated in track and field during the spring, running sprints for the Buffs.
Losing Carr is big for the Buffs, as he was expected to compete for a starting role in the fall.
Even without Carr, CU has a crowded and talented backfield. Juniors Michael Adkins II and Phillip Lindsay are both over 1,000 yards in their careers. Adkins has rushed for 1,145 yards in 22 career games, while Lindsay has 1,044 yards in 25 games.
Another junior, Donovan Lee, excelled last year after shifting to running back from receiver, picking 286 yards on 49 carries.
CU also has incoming freshman Beau Bisharat, who, at 6-foot-2, 210 pounds, is the biggest running back on the roster. Redshirt freshman Dino Gordon could also be in the mix, but he is currently suspended and working his way back to the team after an off-the-field incident this offseason.
Walk-on Kyle Evans has shown some flashes, too. He had 52 yards and a touchdown on 18 carries last season, with almost all of that coming against Nicholls State.
Contact staff writer Brian Howell at firstname.lastname@example.org or twitter.com/BrianHowell33.