California Highway Patrol Officer Leland Tang said Odom was unable to complete a field sobriety test, and once at the station he refused chemical tests to determine his level of alleged intoxication.
Drivers suspected of DUI may refuse to take tests in the field, but once they are at a police station, they are required to take a chemical test. If they refuse, they lose their driving privileges for a year.
"He did the one thing you should never not do: refuse the chemical tests," Tang said.
By obtaining a California driver's license, drivers consent to have their breath, blood or urine tested if they are arrested on suspicion of driving under the influence of alcohol or drugs. A driver does "not have a right" to consult a lawyer beforehand, according to the California Department of Motor Vehicles.
"If you refuse to submit to any of the tests, your driving privilege may be suspended because of your refusal," according to the department's handbook. It adds: "Even if you change your mind later and agree to a test, and your BAC [blood alcohol content] measures 0.01% or higher … your driving privileges may be suspended for both reasons."
Odom was released Friday morning after spending about 3½ hours in jail.
The 33-year-old basketball star was released after posting $15,000 bond and is expected in Van Nuys Municipal Court on Sept. 27.
The 6-foot-10 forward, who most recently played with the Clippers and is now a free agent, was arrested early Friday after a California Highway Patrol officer observed him driving erratically on the 101 Freeway in the San Fernando Valley, Tang said.
CHP officials said Odom was in a white Mercedes sports utility vehicle eastbound on the 101 Freeway near Sepulveda Boulevard just before 4 a.m. when he was spotted driving below freeway speeds, at about 50 mph.
A CHP report notes that Odom was driving in a "serpentine manner." He showed signs of being under the influence of either drugs or alcohol and failed a field sobriety test, according to the CHP.
At the Van Nuys jail, Odom refused all chemical tests and was booked without incident, Tang said. An inventory of Odom's SUV revealed no drugs, alcohol or other contraband, Tang added.
Odom was booked into custody at 5:01 a.m. and released at 8:33 a.m.
His agent, Jeff Schwartz, could not immediately be reached for comment.
Odom has made headlines in recent weeks for alleged drug use, including reports last weekend that he was missing after a fight with his wife, Khloe Kardashian Odom.
His agent told ESPN that the basketball player was "not missing," and a source told the outlet that Odom was at a Los Angeles hotel as friends tried to help him with a drug problem.
Kardashian Odom tweeted about the reports, saying it was "really hard to sit here and listen to people talk … about my family."