If you are buying a property in DC and otherwise qualify for the Homestead Deduction, you will still qualify even if your parents, who live somewhere else, are co-owners with you.
As a benefit to homeowners living in a property as their principal residence, the DC Homestead Deduction subtracts $69,100 from the assessed value of the property before real estate taxes are calculated.
As long as you are a co-owner and will live in the property as your principal residence and will be domiciled in DC, the fact that your parents are also co-owners but are not living in the property will not matter.
You will be the applicant and will sign the form. You will need to include your parents’ names and social security numbers on the form, but they do not need to sign the form.