The Roth vs not debate is irrelevant to the question. It doesn't matter where your emergency fund is kept, as long as it is liquid and safe.
I said it before in an answer to another question:
your emergency fund is not an investment -- it's your safety net
This answer also says it well:
an "emergency fund" is just that... for emergencies... NOT investment.
While it "hurts" not to have your emergency money making more money... its MORE IMPORTANT to have quick access to it.
So at TD Ameritrade, just park it in their FDIC deposit account. It will not earn any meaningful interest (at least until rates rise), but you'll be able to have access to it when you need it.
Note that I would caution against putting it in a money market mutual fund. They're safer than many other investments, but they're not FDIC insured against loss and there is a potential for temporary loss of liquidity.
In late 2008 when the credit markets collapsed, a lot of people suddenly became unemployed -- and needed access to their emergency funds. When Lehman Brothers went bust in September, the Reserve Primary Fund (with billions of dollars in their fund) "broke the buck" -- they lowered the price of shares below $1, meaning investors lost principal. The worst part is that investors were not as liquid as they wanted to be: the fund froze and it was hard to get money out.
The lesson to take away from this is that one of the times you're likely to need access to your emergency fund is during a macroeconomic crisis. This is also the time when any investment that isn't guaranteed safe may potentially be (at least temporarily) unavailable or decline in value. Emergency funds should be 100% government insured.
When you have your Roth funded to the point where there's extra money beyond the emergency fund, you can start investing in higher-yielding vehicles: stock or bond index ETFs would be a good start. But then that part of your Roth starts to look like a retirement account and not an emergency fund.
If it were me, I'd open a Roth at a stable local bank and just keep it in their FDIC insured money market deposit account. Then if I wanted a slight boost, I might put the "upper half" of my emergency fund into short term CDs, but even CDs aren't worth much at the moment.