My sister & I bought a home 50/50 We are on the deed jointly, and we have no written agreement other than the closing documents. She paid for her half of the mortgage for 2 years, then paid nothing for the past 3 years, during which time I have been paying the full mortgage amount and all other expenses. If she has not been contributing any money towards the property for the past 3 years, in other words she has not continued her half of the mortgage is she still entitled to the full 50% of the equity?
There are two roles here: Owner/landlord and tenant. You are both co-owners/landlords, and you alone are the tenant. There's also the separate issue of what to do about the refinance.
Regarding the ownership role: You and your sister should have been contributing to all owner expenses including the mortgage and major repairs equally, but NOT including normal tenant expenses like utilities. Add it all up for both of you, and assuming you've contributed more than she has, she should owe you that amount to make it equal.
Regarding the tenant role: You should have been paying a fair market rent to the owners (including yourself) over all this time. Figure out what that is, then you owe your sister half of that.
Regarding the re-fi: You need to buy your sister out. You should pay her half of the equity. It might be possible for you to role this into the loan, but not all lenders will do that. In this case you would end up borrowing more money with the new loan than what you owe on the original, and you can give your sister the money out of closing.
Edit: Determining equity during a re-fi can be tricky as it will depend on someone's opinion of the value. Your lender will require you to get an appraisal, so it would be pretty reasonable to use this value - but you or your sister may not agree with that value. In that case you might try getting another appraisal or two and average them or take the one in the middle.
If you sold today, a title agency would be responsible for distributing funds equitably. They will make sure fees are paid to the appropriate agencies, any liens are paid off, and other participants in equity are also paid. Most frequently this is the real estate commission.
Money left over, is then distributed to the owners. This would be done in accordance with any business agreement in place. Failing any such agreement they would split the money between owners, or in many cases as a jointly cashable check (typical for married couples).
So failing any legally binding business agreements or agreements you can reach with your sister the proceeds would be distributed equally.
You can then sue your sister for not participating equitably in this business venture but in that case you are best to seek legal advice.
I am refinancing to become the sole owner...
No, you are not!
How can you become the sole owner without the permission of the other owner? If you and I went splitsies on a hobby-horse, you can't call Fisher-Price Finance and take away my ownership, unless the finance company foreclosed on us both.
As other commenters have noted, if you want to be the sole owner, you could say, "Sis, I would like to buy you out. Here's what I think is fair, given your contributions, my contributions, and my use of the house." Then, negotiate.