Yes. To home school legally in Utah, you must submit an affidavit to your school district.
You can begin homeschooling your child anytime during the year. You just need to submit an affidavit to your school district. They must accept your affidavit and provide you a certificate of exemption, no matter what time of year it is.
It is not uncommon for many school districts to be slow in returning certificates of exemption. If it's getting close to the start of the school year, or if you are just feeling uncomfortable, call your school district's homeschool liaison or drop by their office.
The compulsory education law states that children who have turned 6 years old but are not yet 18 years old must attend public or private school, or be exempted for home school. The cut-off date for public school registration in Utah is September 1 of each year. Any child who is 6 years old by September 1 must receive exemption from attendance.