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Can you please be a little more specific as to what you are referring to as "US property"?
Are you referring to US stocks or bonds or US houses/real property?
House - real property
This is a simple answer but is actually quite complex. I'll give you the simple answer and you can ask further questions in this chat as you need to get further clarification.
Basically investing in US real property will subject you to US taxation on the rental income and gain on the home sale. The tax rate will be between 15 and 20% as there is a treaty between the US and Canada. Generally speaking foreign persons do not invest directly in US real property as it does not provide for favorable tax rates. Instead foreign persons would invest in the real estate through a US corporation, thus shielding the foreign person from US taxation. (the US corporation is the one subject to tax)
See links here for some more "light reading":
What conclusion from the IRS site: If Canadians or foreign persons have an Active Income from US real property(material. participate, paid propery tax ect),so for them work Tax Rule as US citizen, isn't it?
I do not really understand your question. But if you are actively participating and managing the U.S. rental property then you will be considered as doing business in the U.S. and subject to U.S. income taxes on the U.S. source income you receive just like a U.S. citizen.
Please let me know if I can provide additional clarity somewhere to best answer your questions.