Is it a good thing to sign the deed over to the mortgage company? Does this help the credit process?

The only pro would be if you have a homeowners or condo association, the future maintenance will be your personal debt and you are liable for any POST filing of the bankruptcy case HOA/Condo fees. If there is NO HOA/Condo, then why bother with a short sale. Your debt to the mortgagee is already discharged and the foreclosure would not affect you as that debt was included in your bankruptcy case (if it was listed on you)

Yes, a foreclosure most likely will be noted on your credit report. Be very careful about a short sale. Talk to a good foreclosure attorney.

I am going to assume you filed for Chapter 7 and there are no HOA fees involved. Advantage of a short sale is if they will give you some $$ to move out. Otherwise, neither should affect your credit report in any way because your personal obligation was extinguished in the Chapter 7.

If you want to get rid of your house by signing the deed over to the mortgage company, you will have to have the permission of the mortgage company. Why? Because the mortgage company can look a gift horse in the mouth and may be unwilling to accept your debt in case there are known or even unknown liens on the property, such as taxes, HOA obligations and other problems. While a foreclosure may not show up on your consumer credit report (unless the foreclosure is by judicial process) because of your bankruptcy, it will show up on an insiders report of foreclosures & will make it difficult for you to obtain new mortgage financing. If this mortgage is federallly insured, the CAIVRS program may even put you on a secret blacklist preventing you from obtaining a new mortgage. So a short sale may be your best way to prevent this problem, but of course, you can't short sell unless the mortgage company agrees.