Mr. Smith and his brother, Thomas, founded Taser in Scottsdale, Ariz., in 1993, and the company now is worth about $1.3 billion. Taser cameras have captured thousands of altercations between the police and the public and several controversial police shootings, including ones in Albuquerque and Cincinnati.

Image Axon body cameras are worn by officers in dozens of big cities including Los Angeles, New York, Chicago, Washington and Dallas. Credit... Caitlin O'Hara for The New York Times

Yet as Taser works to sell cameras and software to more departments, it is coming under fire for questionable business practices. In some instances, it has paid police chiefs to travel to Taser conferences. In other cases, chiefs who have bought Taser products have joined the company as consultants shortly after leaving public service. And several cities have awarded contracts to Taser without competitive bidding.

So far, these issues have done little to blunt Taser’s momentum. Last quarter, for the first time, Taser booked more sales for body cameras and related software than it did for its stun guns.

Interest in body cameras was already picking up two years ago, as police departments around the country started responding to calls for greater accountability. Then, in August 2014, a white police officer killed Mr. Brown, an unarmed black teenager, in Ferguson. The officer was not wearing a body camera, and witnesses disputed his account of the altercation that led to the shooting. The officer was not charged, and critics said that had he been wearing a body camera, the outcome might have been different.

Video captured by body cameras can be difficult to interpret. Yet as more Taser cameras are deployed around the country, the grainy images they produce are playing an increasingly important role in the aftermath of deadly shootings.

At times, the video can exonerate officers. In 2009, shortly after Taser began selling its cameras through its Axon division, Sgt. Brandon Davis shot and killed a man in Fort Smith, Ark. Video recorded by his body camera captured the shooting, and Mr. Davis was cleared of wrongdoing.

In other instances, the footage can portray police as needlessly aggressive. In 2014, a Taser Axon camera worn by an officer in Albuquerque captured the fatal shooting of a homeless man by officers who did not appear to be threatened. The two officers have been charged with second-degree murder and are expected to stand trial soon.