Every private is different. It is important to check each University's website to see their own deadlines and requirements. 

Many private universities use the Common Application as the application document they require from students. Learn more about the Common App here: https://www.commonapp.org/

Some private universities require students to complete a CSS profile to be eligible for university scholarships. Learn more about the CSS profile here: https://cssprofile.collegeboard.org/ and use the following link to view with institutions require the CSS profile: https://profile.collegeboard.org/profile/ppi/participatingInstitutions.aspx