Police are investigating whether protesters are criminally liable for covering a police motorcycle with handbills and blowing a whistle by an officer's ear. The incidents happened at the July 1 march.
Photos of the two incidents have been widely circulated on the internet. They have stirred debate about the behaviour of protesters.
One picture shows a police motorbike covered with protest handbills. Another shows an officer shrinking back as a man blows a whistle close to his ear.
The police said the cases were being investigated. No one has yet been arrested.
A riot policemen's group said many officers were unhappy about the pictures. They felt insulted when protesters swore at them.
'It's basic manners to respect each other,' said Joe Chan Cho-kwong, chairman of the Junior Police Officers' Association. 'We are used to all kinds of shouting and offensive words when it comes to triad crimes, but when they come from an average person, we can hardly accept that.'