The quickest way to get your state refund is to file your taxes electronically and have your refund deposited into your checking or savings account. For those who file electronically, a refund takes an average of 2 weeks. However, if you mail in your state tax return, it can take up to 10 weeks.he quickest way to get your state refund is to file your taxes electronically and have your refund deposited into your checking or savings account. For those who file electronically, a refund takes an average of 2 weeks. However, if you mail in your state tax return, it can take up to 10 weeks.