To have or not to have will depend on branch of the Police total force.  The ones you see often are Traffic Police, and  they do not.

If the security guards for cash drops can carry shot guns and assault rilfes then i would assume the police would have an armed response unit too, but western common sense r@rely makes any sense here

In Tianjin you see a lot of armed police. There are police in the subways with submachine guns. Also in some of the tourist areas there are police with assualt rifles. Some of the normal police have pistols but not all of them. I guess it depends on the city. Being China there is no standard set of equipment. I find it weird but Tianjin police are too heavily armed in my opinion.

A few with pistols.

I do remember a lot of AKs up in Shenyang, but then again, the army is up there so...

On average, most don't have weapons.

Only the properly trained and certified police (usually a kind of Chinese SWAT) carry weapons... or those that do currency transport etc.

The traffic police obviously don't and the cheng guan are just hired thugs. A lot of other police officers aren't police either but just peasants that were hired because they were friends and family of someone... or bought the job. 

This is why nobody in China fears them. Because they aren't real police... (in the sense they received proper training from a police academy or even know how to fight). Most of them are just countryside folk in a uniform.

Ordinary police in China generally did not carry a gun. As a consequence of last year knives assaults this was changed and the police in major cities is now armed.
I frequently see police officers with pistols.

Typically, your average officer is not allowed to carry firearms, let alone traffic cops. But it has changed after the terrorist attacks last year. Now some of the ordinary cops can carry guns.

Some units, more or less the SWAT equivalent have automatic weapons, but you don't see them on streets unless there is an emergency.

I have seen armed military escort with some heavy machine gun alongside the local brink trucks.

In Guangzhou after the terrorist attacks in the subway there were heavily armed soldiers patrolling around and inside the stations, sometimes even inside the trains.

somebody  once told me they leaves theirs in their locker because it was more trouble than it was worth

I have only ever seen armed police downtown around stations etc, or when there is a high ranking suit visiting.

Apart from the cash delivery guy, I have never seen guns on general Police.

But a few months back, my sister in law came rushing into our apartment saying there was a mad man downstairs ranting at people, the Police turned up, she ran away, and then she said she heard a bang. She said the Police shot him.

I went downstairs to see, and there was nothing to see. I would have imagined if Police had shot a mad man there would at least be a bit of gossip, but no.

I suspect the bang she heard was the police van door being slammed shut.

But I do find it interesting that the Police are not armed here.  I will ask some people why not?

How many Chinese Police have you seen with a gun, Scots? Policemen do have them of course. Being a eunuch is no longer a requirement to work in the government. Their guns are smaller than average, I'm told.

A report cites three different times that service weapons were left in bathrooms and other spots across the complex. In one instance, a child visiting the Capitol reportedly found a loaded Glock.

Headlines from the US moments ago...

Imagine if Chinese police had guns...

.

Apart from at airports and cash deliveries, the only time i have seen police with guns was when I was at a local football match at the Beijing Workers Stadium, there they were in full riot gear and dogs.

The stadium was only 1/3 full (the match was terrible) and there were more than 4 times as many police as there were players on the pitch.