I suppose it depends on the sport (I assume you are talking American Football). Here are the NFL rules
. I think the red section answers your question.
OVERTIME RULES FOR NFL REGULAR SEASON
At the end of regulation, the referee will toss a coin to determine which team will possess the ball first in overtime. The visiting team captain will call the toss.
No more than one 10-minute period will follow a three-minute intermission. Each team must possess, or have the opportunity to possess, the ball. The exception: if the team that gets the ball first scores a touchdown on the opening possession.
Sudden death play — where the game ends on any score (safety, field goal or touchdown) — continues until a winner is determined.
Each team gets two timeouts.
The point after try is not attempted if the game ends on a touchdown.
If the score is still tied at the end of the overtime period, the result of the game will be recorded as a tie.
There are no instant replay coach’s challenges; all reviews will be initiated by the replay official.