Weren't there police in China in the 20s?

Good Question, Im sure there was some sort of Authority all cultures have them but how much they cared about what a men did to his wife differs. Asking that question is like asking if police were in america while african american were being lynched and killed in the south from 1880 to 1960 or Native American treatment and the list goes on in America alone. Of course we had police, people with authority and a court system. Its just that they turn a blind eye to illegal actions sometimes.
Also you have culture relativism and some culture dont considered it murder in cases of this or that. Though i dont think thats the case here, it might be.

There were definitely police or some sort of authority in China during the 1920s. The cities at that time were actually much more progressive, this movie is set in a more rural setting, so there are differences between the two in terms of how such a murder would be perceived. Also it is possible that a wealthy man could get away with something like that if it was kept secret if the servants and other wives were not allowed to talk about it or his wealth could buy off any punishment.

You are assuming that infidelity was not a capital offence in 1920's China, it it probably was. Hey it is still in much of the middle east right now! It's only punishable if it's illegal!

The police is extremely unneffective in third world countries.

I should know, I live in one. (Brazil)

While an authority could have been summoned, the humiliation of investigation would have been enough to quiet family members who knew about the circumstance. Also, local workers outnumbered available jobs. The fear of losing a stable job (that feeds their family) would be enough to keep any servant from exposing the crime.If their master is in prison, they have noone to work for. If he is absolved of the crime, they would likely be turned out as soon as possible because of their betrayal.

In this case, it's important for one to remember that law is only as good as it is embraced. A person generally can't be punished for a crime they've committed if their victim (or in the situation of murder,witnesses) refuses to talk and evidence is scarce. China in the 1920's was not kind to those with negative attention brought to their name,justified or not.

The Chinese government was exceptionally weak during the 20s [and 30s, and 10s]. It is highly unlikely that actions such as in the movie would be punishable by a central authority [combination of weak government, rural setting, exceptionally powerful perpetrator].

I believe warlords controlled some parts of China during that period.

in a word, no. since the overthrow of the qing dynasty and the establishment of the republic of china in 1911, much of the country gradually fell under the control of regional warlords. by the 20s, the country was in shambles. the warlords controlled most of the north and the internationally recognised capital in beijing while the kuomintang, in its newly established capital at nanjing, held a fragile alliance with the communist party of china and the southern warlords. it was not until the late twenties, after the northern expedition (the all-out military conquest of china by the KMT army from its base in the south) and the subsequent unification of the country under chiang kai-shek, that law and order were eventually restored. unfortunately this stability was relatively short lived as the japanese began to seize chinese territories in the 30s and tensions between the KMT and the CPC gradually degenerated into all out civil war.