I want to sell a rental home that belongs to me and my wife. She has dementia can I sign for her and myself?

You need to go to court and get a conservatorship.  It's too late for a POA.

Only if you have power of attorney over her assets

You cannot sign her name unless you have power of attorney. 

If her name is on the deed then you will need a power of attorney authorizing you to act on her behalf because of her incompetence at the time. It can also depend on how bad her dementia is. Sometimes they can still be together in their mind at times so she can actually understand what you are asking. 

No, unless you have her mental power of attorney.  Otherwise, you would be committing fraud.  You must have heard of forgery? !!!

Not unless you get a power of attorney or get her legally declared incompetant by the court. 

Not unless you have power of attorney for her.

If the land is owned by Me AND my wife, then you need both of you to make decisions. 

If the deed is held Me OR my wife, you can sell it without her authorization.

Since she has dementia and unable to make decisions for herself, you need to go to court and get conversatorship of her. 

Unofficially, if she can still sign her name, you can have her sign a power of attorney document.  This is NOT legal since she can't make decisions for herself anymore but it's done every day.

Only if you have POA for your wife

only if you have Power of Attorney.  with mild/early dementia, she can still make decisions for herself.