If you were still legally married as of December 31, 2016, you are able to file a joint return or you can do married filing separately.
While you will generally pay lower taxes overall if you file a joint return, you may still wish to file a separate return. This would particularly apply if you do not want your spouse to know your personal financial details.
Filing a joint return will not give your spouse any rights to the house you purchased separately using your own funds.