> To make things really simple, we could file both federal and state tax
> separately. But because I live in a communal property state, if I file
> the federal tax separately, I am supposed to only include half of my
> salary in the tax return, right?

Yes

> Does my spouse then need to add the other half of my salary as her
> income in her federal return?

Yes

> Does she need to file state tax in my state as well since she's now
> getting half of my salary as her income?

Yes, since it's CA-source income.

Let's consider the different options.

If you file federal taxes MFJ:
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 - You guys will file CA taxes MFJ using form 540NR, since one spouse is nonresident. It will include all of your income and none of your spouse's income. The tax rate will still be based on the total income of both of you.

 - For CT taxes, you have two options:
   - You guys can file MFS (i.e. you spouse files MFS and you don't file) since one of you is a CT resident and the other a CT nonresident. Your spouse's return will contain half of your income and all of her income. 
   - You guys can choose to file MFJ, treating you as a CT resident. Your return will contain all of your and her income.

   In both cases, a CT-1040 return is filed, and a tax credit can be claimed on it (with Schedule 2) for the taxes on the income taxed by both CA and CT (i.e. your income or part of it).

If you file federal taxes MFS:
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 - Your federal tax return will contain half of your income, and her tax return will contain half of your income and all of her income. The total taxes will almost certainly be more than with MFJ.

 - You will file CA tax MFS with form 540, including half of your income. She will file guys will file CA tax MFS with form 540NR, including half of your income, but her tax rate will be based on the total of half of your income and all of her income.

 - She will file CT tax MFS and you don't file. Her CT return will contain half of your income and all of her income. A tax credit can be claimed on her CT return for the taxes on the income taxed by both CA and CT (i.e. half of your income).

So as you can see, you don't really gain anything from filing MFS for federal, and potentially stand to lose from filing MFS since the tax brackets are designed so that MFS always has equal or more taxes than MFJ for a given combined income (without considering credits and other things).

With federal MFS, you file MFS for CT, but with federal MFJ, you still can file MFS for CT, and in fact, you have the option of MFS or MFJ for CT, and choose whichever one is better, so you don't lose any options for CT and gain more options by doing federal MFJ. And for CA, no matter if you file MFJ or MFS, the total amount that is taxed is your income; the comparison of tax rates is more complicated with your spouse's tax rate based on her whole income, but MFS is still unlikely to be better than MFJ for CA.