The allegations of mistreatment were reported to police and the RPSCA, which has investigated but taken no further action.
A spokeswoman said the charity was “aware” of the allegations but “unfortunately we are unable to discuss complaints about specific people”.
Several police vans could be seen in footage of the protest as officers took the dog out of the property while protesters cheered.
The dog, which appeared to be a German Shepherd, was taken to police kennels, the police spokesman said.
“We would urge residents to refrain from making speculative comments about the incident online as our work continues with the RSPCA and Manchester city council,” he added.
