One of the issues you are going to face, being "only" separated, is the uncertainty of what is going to happen due to the eventual divorce. In other words, are you going to be told to pay child support or alimony; for what amounts; which debts are you going to have to take on and which will your spouse? With all this uncertainty, lenders are going to be reluctant to give an approval.
This is in addition to the answers below. You will need your spouse (you are still married) to sign on the loan or sign-off on the disclaimer, if you can get approved. Remember, not telling your full financial story is committing mortgage fraud.
In Arizona, a community property state, until you get a divorce, or a judge to rules that your are no longer man and wife and responsible for the other's debt, your finances are intertwined. You are responsible for her debts and she is responsible for your debts. You really need to get legal advice and not rely on our answers in this blog.
As was proposed you can have your spouse sign a Community Property Disclaimer Deed (aka Spousal Disclaimer) where your wife waives any rights to this property. But as long as you are married, you can apply for a loan in your name only, and the lender will insist upon look at your spouse's debts (since they are your debts as well) and she will need to agree in writing to let them search her credit.
You may not want to hear this, but it might be best for you to rent until your marital situation is settled. This can be a tough time and your needs and situation may change your housing and financial situation. Talk to your attorney before you make a final decision.
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