In most countries, government works on several levels.
There is generally some central government which governs matters concerning the whole country, and then there are some matters which are devolved to a more local government. Generally each level of government manages a budget for the services under their care. In the UK for example we have county councils which deal with a region of the country and govern things like education; then we also have smaller borough councils that deal with things like refuse collection.
In the US and Canada I believe the highest level of government is federal (because the countries are a federation). I also understand that in the US the areas that comprise this federation are states, and in Canada they are provinces.
So in your example you use the terms federal and provincial governments, but you go on to speak about "state" support and "municipalities".
Unemployment soared during the 1913 depression, but federal and provincial governments refused state support, and argued that responsibility for relief should remain with the municipalities.
The term "municipal" relates to the government of a town or district, which in some countries such as France is a much smaller area than what you might call a "state" in other countries.
All I can say is that you need to check your terminology is correct for the country you are writing about.
I have heard the term "state support" meaning financial support provided by a state-level government in the USA. But in a country where they do not use the term "state" they may not use this terminology (although in the UK we don't have "states" yet do refer to our welfare system as "the welfare state").
I'm not an expert in the governmental structure of every country, but I would say that "state support" can only refer to one level of government or another, so it doesn't seem correct that you apply to it both to federal and provincial. I would remove the word "state" and just say those two levels refused support and said it should come from government at municipal level.