SARATOGA SPRINGS, N.Y. -- Chad Brown, a four-time winner of the Eclipse Award as champion trainer, was arrested by Saratoga police on Wednesday night on a misdemeanor charge of obstruction of breathing, according to the Saratoga Springs police department.  Brown, 43, appeared before a judge on Thursday morning for his arraignment, where the assistant district attorney Kayla Potter said that he had pushed a woman down a flight of stairs at his home, pinned her to the ground, and tried to choke her, according to local reports.   Brown pleaded not guilty and was released on $2,500 bail and a $5,000 bond. His lawyer, Joseph Gerstenzang, told the judge that the woman had broken into his house and that Brown was defending himself.   Sgt. Paul Veitch, a spokesman for the Saratoga police, said that he could not comment on the incident that led to the arrest.  “This is still an ongoing investigation,” Veitch said.  According to sources, the alleged victim is an exercise rider and she was at one time romantically involved with Brown.   Pat McKenna, a spokesman for the New York Racing Association, which operates Saratoga Race Course, said in a prepared statement that “NYRA is aware of the charge brought against trainer Chad Brown today and will defer additional comment on this matter to the Saratoga Springs Police Department.” Brown was not at Saratoga Thursday to saddle Nabokov for a first-level allowance race. However, Peter Brant, the owner of that horse and a bevy of Grade 1 winners trained by Brown, was at the track and said based on accounts of the incident he’s been told, he is “totally supportive” of Brown. “He’s not a person that would do something like that unless he was provoked,” Brant said. “I think he was protecting himself. I think he’s a smart guy with a lot of sense. I was told he was woken up by this person and [she] started to hit him. He was obviously just protecting himself.” Brant added that Brown “has to have a right to have his day in court.” On Thursday, the judge in the case granted an order of protection to the alleged victim allowing only “incidental contact” between herself and Brown, citing the fact that both work on the Saratoga backstretch. Daily Racing Form is withholding the name of the alleged victim, who declined to comment on Thursday morning.   Gerstenzang did not immediately respond to a phone message. According to New York’s penal code, “obstruction of breathing” is defined as applying pressure on the throat or neck of a person with the intent to impede normal breathing or circulation of the blood, or blocking the nose or mouth of a person with the same intent. A class A misdemeanor carries a maximum penalty of one year in jail or three years of probation. Brown is a native of Mechanicville, a town near Saratoga Springs. He is one of the most high-profile trainers in the country. Earlier this year, he won the Preakness Stakes with Early Voting. Early Voting is one of three horses that Brown is pointing to the Aug. 27 Travers Stakes at Saratoga, along with Zandon and Artorius. He is currently leading the Saratoga trainer standings with 27 wins.   Brown has two horses entered on the Thursday card at Saratoga, and seven horses on the Friday Saratoga card. On Saturday at Saratoga, he has seven horses entered, including four in the Grade 2 Lake Placid Stakes and one in the Grade 1 Alabama, the 3-year-old filly Gerrymander. The same day, he has Highly Motivated entered in the Grade 3 Philip H. Iselin Stakes at Monmouth Park in New Jersey.  For the year, Brown has won 168 races from 569 starts, with purse earnings of $19.8 million, highest in North America. He has trained 10 Eclipse Award winners. Brown is divorced and has two daughters. --additional reporting by David Grening