Burgos is accused of abandoning the victims and fleeing, charges that can carry six months to two years in prison, Prosecutor Raul Quiroz told The Associated Press.
"We recommend that Mr. Burgos turn himself in so we can start the judicial process," Quiroz said.
The SUV registered to the reliever struck pedestrians Josefina Minaya Martinez, 38, and Angely Fana, 29, on Tuesday in the town of Nagua, north of the Dominican capital, according to police. The victims later died at a hospital.
Police said witnesses told them Burgos was the driver, even though his cousin Edwin Silvestre Sanchez claimed to be behind the wheel.
Sanchez was released from police custody Friday, but he still could face charges as a possible accomplice, Quiroz said.
Quiroz said Burgos was recently arrested on an unrelated charge of illegal weapon possession, and released after posting a US$3,000 bond.
Burgos also was arrested last month in New York on assault and harassment charges after allegedly throwing his girlfriend to the ground. He has appeared in court on those charges but did not enter a plea, according to prosecutors. He's due in U.S. court again Oct. 23 and faces up to a year in jail if convicted of the more serious misdemeanor assault charge.
The 24-year-old Burgos has not appeared in the major leagues since last year and spent the past season on the disabled list following elbow ligament replacement surgery. He pitched in the minors last month while on a rehabilitation assignment.