The incident happened at Gateway Apartments Thursday evening.
The video shows the man chasing the dog down a hallway, then punching and kicking the animal and dragging it away before disappearing from sight.
The footage has outraged residents of the building and local dog owners, who are calling for the man to be found and arrested.
Anaheim police Sgt. Shane Carringer says the department has been flooded with calls as investigators work to find the man and the dog.
"We absolutely appreciate the passion that people have for this circumstance, however, we ask that they temper their passion and have some confidence in our abilities to solve this crime, to investigate this crime," Carringer said.
He said because this case has garnered so much public interest they've had people wrongly name others who have nothing to do with this investigation as a possible suspect.
Carringer said that puts people in harm's way.
"There's a lot of keyboard investigations going on that is misidentifying people that have nothing to do with this incident, nothing to do with the circumstance and they may be thinking that they're assisting law enforcement at this point but they're not," Carringer said.
Also, he added detectives know the name of the man seen in the video and are actively looking for him.
Anaheim police is asking for help in finding the dog to make sure it's OK.
"There are people out there who still may not know about this case, and they may have gotten a dog recently that they thought was a gift or found a dog that was abandoned," Carringer said. "That could be the dog that's in question."
Carringer said they're looking for a possible black Goldendoodle or Labradoodle, medium to large in size.
He said once they find their suspect criminal charges could be filed. They say he could potentially face felony animal abuse charges.
"Our goal in this, and any criminal investigation, is to collect all available evidence and facts in order to have the most complete investigation possible," said police in a statement posted on Instagram. "To that end, our detectives continue to work on this case."
Anyone with information is urged to contact Anaheim police at 714-321-3669.