Det. Michael Eisenloffel, of the Nye County Sheriff's Office, said in an application for a search warrant to take Odom's blood that he had probable cause to believe the former Laker was under the influence of a controlled substance during his stay at the legal brothel.
Investigators have since taken a sample of Odom's blood, but results were not immediately available.
Odom, 35, was found unconscious at the ranch on Oct. 13, following a four-day stay. He's now recovering in Los Angeles at an undisclosed location. His current condition was not clear.
Eisenloffel said in an affidavit that eyewitnesses claim Odom was "ingesting an unknown substance in the form of an unidentified pill, which he obtained from his pocket" and that he "possibly ingested cocaine" after prostitutes "heard him snorting."
Police also cited Odom's "prior history of illicit narcotics use" and that Odom's personal assistant indicated he "has actually witnessed Mr. Odom under the influence of narcotics."
Eisenloffel reiterated that when Odom was found, he had "a white substance coming from his mouth as well as bleeding from his nose," which, from his training and experience he recognized as evidence of an overdose.
His family released a statement on Tuesday, calling his progress nothing short of "miraculous," adding he had even taken a "few steps."
"We couldn't be more overjoyed! We realize Lamar's continued improvement will not be easy, however his unrelenting strength and faith in God will pull him through," the rep for the Odom family told ABC News.