Two police dogs with the Braintree Police Department have been put down and a third taken out of service after the dogs attacked two officers and a child in separate incidents, the department said Monday.

The three attacks prompted the town’s police chief to shut down the patrol dog unit and order a review of its operations. For now, Braintree will keep only its fourth police dog, named Lucky, to help detect illegal drugs.

“There is a certain risk when deploy­ing canines, not only to our officers, but to our citizens as well,” said police Chief Paul Frazier. “The inherent danger associated with their deployment far outweighs the benefit and as such I have made a decision to end their deployment.”

The problems with the Braintree dogs began more than a year ago when an officer was riding in his cruiser with his dog, named Dargo, in the backseat.

The dog became excited when he saw another animal outside the car, according to Detective Brian Cohoon, president of the Braintree Police Officers Association. When the officer went to close the sliding door between the front seat and the kennel in the back so the dog would not escape, the dog bit the officer in the hand, according to Cohoon, whose brother is on the canine unit.

Dargo had been with the ­officer for over four years. The unexpected aggression prompted the department to conduct a medical review of the dog, and police soon discovered that Dargo had a genetic disorder.

“[The officer] made the decision to put the dog down,” ­Cohoon said.

The officer got a second dog, named Yento, soon thereafter. According to Cohoon, the dog had not yet been trained when another biting incident ­occurred.

The dog was at home with the officer’s wife and son, who is about 5 years old, Cohoon and Frazier said in separate inter­views, when it was taken out to relieve itself.

The toddler startled the dog, and it bit him. According to ­Cohoon, the child required stitches, though his injuries were not serious.

“The Weymouth police were called and the arriving officers choked the dog to get it off their son. The dog died as a result of the officers’ actions,’’ Frazier said by e-mail Monday night. “Short of shooting the animal, I believe this was the only course of action the officers could take’’ to save the officer’s son.

The same officer received a third police dog after that incident, and the department did not have any additional issues until April 28, when another ­officer was attacked by another dog.

According to a news release from the department, the third biting incident occured when Officer Kristine Lydon responded to a call to help find two missing children. Officer William Cushing, Jr. brought along his police dog, Kitt, to help in the search.

Officers found the missing children and were about to leave the scene when Kitt climbed out of an open window of a police cruiser and attacked Lydon.

Lydon suffered a serious leg injury and was transported to Boston Medical Center, police said. She underwent surgery and was later released from the hospital. Cohoon said an infection from the incident has complicated Lydon’s recovery. ­Although she is getting better, she is not expected to return to work for a couple of months.

The three incidents prompted Frazier to shut down the depart­ment’s patrol dog unit entirely. The unit will be ­reviewed before deciding if any police dogs — or canine units in police jargon – should return to work.

Frazier said the step was necessary for public safety and the future financial health of the town.

“If this was a member of the general public, the town could be sued,” Frazier said. “I trust in the future that a thorough independent review of the canine program will be conducted before any decision is made to ­reinstate the program.”

Cohoon, who started the ­canine program in 1991, said it is unfair to disband the police dog department because of the episodes. “It’s a successful program, a good program, and it’s an unfortunate accident and it comes down to handler error,” Cohoon said.

Town officials did not respond to requests for comment.