Do you have any dependents or children? You can't check the HOH box until you have entered dependent info and ssn. Enter them under My Info. Then Turbo Tax will automatically give you Head of Household if you qualify.
See IRS Pub 501 page 10 for qualifying person.
https://www.irs.gov/pub/irs-pdf/p501.pdf
Head of Household doesn't mean where you live or if you own a house. Just that you are single or considered unmarried and provide support for a qualifying person (not a spouse or non-relative).
Start by choosing Single or Married Filing Separately and when you enter a dependent, if you qualify it will change it to Head of Household.