My mother passed away in June 2016 and my father passed away January 2017. Do I file jointly - it doesn't show deceased anywhere. Do I sign?

So sorry to hear of your parents' passing.

Yes, your parents' return may list married filing jointly. The 2016 return should list your mother's death, with your father still alive. Your father's final return will be filed next year for the 2017 tax year. His filing status would be single (or qualifying widower if he had dependent children) and you should report his death on that return.

To report your mother's death, scroll to the very bottom of the page headed Your spouse's personal info. When you click Yes to My spouse passed away before filing this return, you will then be asked to type in the date of her death. (Click on the screen shot below.)

If you have followed these instructions, then all should be well, and you should see "Deceased" printed at the top of the form.

Before you file a decedent's return:

1. Make sure the Social Security Administration has been notified of the taxpayer's death. You can either go to their website  or call 1-800-772-1213.
2. To prevent an e-filing rejection, when you enter your parents' address, write In Care Of with your name and your address.
3. If the refund is to go to you, you must file Form 1310. You can find that form by typing "Form 1310" in the Search box.
4. Many (but not all) states allow decedent tax returns to be e-filed as well. We'll let you know when you get ready to e-file the state return.
   

If you are filing both your return and your parents' in TurboTax, you will need to create another account in order to file another return. You can see the instructions in the TurboTax FAQ below to do so:

https://ttlc.intuit.com/replies/3288574

This article explains more about dealing with a death in the family.

That is helpful, but since he is deceased he cannot sign his return.  Do I sign in place of him with my name?

I edited the answer - check again.

Because you don't actually "sign" a return when you e-file, what you use to prove identity is your father's PIN from last year and/or his AGI from last year's return. If you have those, you are good to go. Otherwise, you will have to sign your name as executor of your father's estate and mail the return. If the IRS chooses to question you, they will ask for his death certificate, but do not send it when you mail his return. You WILL need to send copies of his 1099-R and W-2 as well as copies of your mother's. Her income that must be reported on the return is only what she received before she died. The rest is "income in respect of a decedent" and belongs to her estate.