The sergeant wrote that Gates initially refused to provide identification, but then showed his Harvard University card. The sergeant again asked him to step outside and Gates allegedly responded, "Ya, I'll speak with your mama outside."
Police said the confrontation was witnessed by the woman who made the call and at least seven other people, as well as several Cambridge and Harvard University police.
ABC News' calls to Lucia Walen, the woman who made the 911 call, were not answered.
Ogletree had a different account of the events, saying that Gates immediately told the police officer that he lived in the house and showed him his identification when he was asked for it.
Gates was on the phone with the Harvard Real Estate office reporting the damage and asking to have it fixed when the officer came to his door, Ogletree said in a statement posted on TheRoot.com.
The professor opened the door to the police officer, but when the cop immediately asked him to step outside, Gates asked him why he was there, according to Ogletree's account.
When the officer told him that he was responding to a report of a breaking and entering in progress at the house, Gates told him that he lived there and was a faculty member at Harvard, the lawyer said.
Rather than denying or ignoring the officer's request to prove what he said, according to Ogletree, Gates said he could and went to get his wallet, which he had left in the kitchen.
Once there, he handed the officer his Harvard University identification and his valid Massachusetts driver's license, both of which include Gates' photograph, the lawyer said.
However, when Gates then asked the officer if he would give him his name and his badge number -- a request he reapeated several times -- the officer did not produce any identification, according to Ogletree's statement.
Instead, the officer turned and left the kitchen without ever indicating whether there were charges against Gates, Ogletree said.
Only when Gates followed the officer outside did the officer say "Thank you for accommodating my earlier request," and then placed Gates under arrest, handcuffing the professor on his own front porch, the lawyer said.
"This is outrageous to us," Sharpton said.
"It's either a clear case of police abuse or racial profiling," he said. "This happens every day, but to have it happen to one of the most prominent black academicians is unbelievable."
This is the third incident in recent months in which blacks at Harvard have accused the school or police of heavy-handed treatment, though the two previous incidents were both on campus.
In February, a woman claimed that Harvard wrongly banned her from the school and barred her from attending graduation ceremonies after she was linked to the murder of a man on campus.
Chanequa Campbell said she was not making an "overall claim of racism," but "I do believe I am being singled out. ... The honest answer to that is that I'm black and I'm poor and I'm from New York and I walk a certain way and I keep my clothes a certain way," she said. "It's something that labels me as different from everyone else."
Prosecutors said Campbell invited the accused killer, a reputed marijuana dealer who was allegedly selling to students, into the dorm where the murder took place.
Months earlier, an African-American teenager, who was caught trying to sever a bike lock on the campus from what turned out to be his bicycle, claimed Harvard police screamed racial obscenities at him.
Gates has been a member of the Harvard faculty since 1991 and holds one of 20 "university professors" positions at the school. He also was named by Time magazine as one of the 25 most influential Americans in 1997.
"I was obviously very concerned when I learned on Thursday about the incident," Harvard president Drew Gilpin Faust said in a statement. "He and I spoke directly and I have asked him to keep me apprised."
The Associated Press contributed to this report.