I follow the instruction of TT on filing with W-7 ie. print out the return and take to IRS assistance center (or mail). What about the state return (CA)? Can it efile?

You will have to mail your CA return as well.  Although state returns can be e-filed with your federal return (or after your federal return has already been accepted), it's no longer possible to e-file state returns before the federal.

This adds an extra layer of security to all e-filed state returns. This also means you won't be able to e-file your state if your federal return was, or will be, paper-filed.

Thanks. do I need to attach W-7 and statement to the state return as well? 

No, only attach and send the W-7 to the IRS. 

For the state return, write "Applied For" in the space for the Social Security Number on the return.

HERE is another answer

I stopped by the IRS assistance center today to submit W-7 form with my spouse passport copy and statements along with my return. However the employees there said that my spouse needs to be present (she resides abroad) and with her real passport, not a copy. I explained my case and they seems confused. They turn to their W-7 booklet and concede that the center is trained to only accept the cases applying for ITIN in person with documents. I was told to call the IRS number. Anyway, I think I'm ready to mail it instead. My questions are below:

1. my spouse passport copy with her local public notary is good enough as foreign status document? 

2. my marriage certificate with English translation and public notarized is good for proof of marriage?

3. do I need to include my spouse birth certificate as well?

4. is it ok for the signature page only a copy? Because my spouse is living abroad I had to email her to sign and send back the copy. 

Your spouse must get a certified copy of her passport from the agency that issued it in her country, or she must send the original document with the W7 to the ITIN processing center.   A notarized copy will not be accepted. 

You do not need to send proof of marriage or her birth certificate with the application.  You do need to send her original signature on the W-7, they will not accept a copy.  

If she cannot get a certified copy of her passport (it isn't always easy to do so), and she's not willing to send the original with the W-7 application, you can see if there is a Certifying Acceptance Agent near her who can assist with completion of the Form W-7 that she can forward to you.  You can find a list of those by country HERE