Investigators are looking into whether Prince died from an overdose and if a doctor was prescribing him drugs in the weeks before his death.
They are also trying to establish whether a doctor was on a plane that made an emergency landing in Illinois less than a week before the singer died and what kind of drugs were on the aircraft and at Prince's house in Minneapolis.
Prince was found unconscious on his plane after it made an emergency stop in Moline, western Illinois, on April 15. He was given a drug used to treat suspected overdoses.
The singer was returning to Minneapolis following a performance in Atlanta when the incident happened. Investigators are looking at whether Prince overdosed on the plane and whether it was an overdose that killed him, and what kind of drugs were involved.
Prescription drugs were found at Prince's home when the musician was found dead on April 21. Results of the singer's post-mortem are not expected for three to four weeks.
Carver County Chief Deputy Jason Kamerud disputed reports that police had asked the US Drug Enforcement Administration for help in the case.
He said: "We have not asked them for help, or asked them to be a part of the investigation.
"We might contact them to help us, but that hasn't happened. We don't have the medical examiner's report yet. We don't know to what extent pharmaceuticals could be a part of this."
Police said the contents of a search warrant for Prince's Paisley Park home and studio, carried out on the day of his death, could harm their investigation if made public.
An affidavit in support of sealing the warrant also warned that disclosing details could cause "the search or related searches to be unsuccessful" and risk injury to innocent people.
Prince's death came two weeks after he cancelled concerts in Atlanta, saying he was not feeling well. He played two shows in the city on April 14 as an apology. Prince was scheduled to perform two shows in St Louis but cancelled them due to health reasons shortly before his death.
Long-time friend and collaborator Sheila E said Prince had physical issues from performing. She said he had hip and knee problems that were the result of years of jumping off speakers in heels while performing on stage.