Investments in the US

I am a Canadian citizen who has returned to Canada after 3 years in the US. I was working on a TN1 visa, while in the US.
I had invested in mutual funds and stocks via US investment companies, while in the US.
Do I have to move these investments to a Canadian investment company, now that I am back in Canada?

Depends to some extent what the investments are, e.g. if you invested in municipal bonds you could have a problem. But the answer is generally no, you don't have to. If they're in an IRA, you have to declare the IRA to the CRA. Under the 2008 tax treaty though, IRAs are treated as RRSPs for Canadian tax purposes, but you must declare them.

The CRA still hasn't invented a form for this purpose, you have to call them.

You need to file W-8BEN with any institutions in the US that are holding the investments as well as your US bank, assuming you moved your tax home to the US and are now moving it back.

Bear in mind if your tax home was moved to the US, there is a fair amount of paperwork involved in moving it back to Canada, such as filing dual-status in the US and filing a pro-rated T1 in Canada next year.

IRS publication 519 explains how to file dual-status. There are various other bits of paperwork you may need to file such as 1040-C.

Thanks for the detailed reply Steve. I have invested only in Stocks and Mutual Funds.
I did move my Tax home to the US, so I will have to go thru the tax forms you mentioned - thanks for prompting me in advance.
Am I allowed to make further investments into my existing mutual funds, with the money I have in my US bank accounts, while living in Canada? Or is that illegal, as I am not a US resident anymore?

If you want to make further investments you do usually need to then use a Canadian registered broker. A lot of US brokers are registered in Canada. With IRAs if there is a legal method of carrying on contributing to them I haven't surmised it, the better method is to simply open an RRSP and if you can, carry on contributing to the same thing you had the IRA in if that's possible (and you want to), depends what it's invested in.