Per IRS Instructions for Form 8965 Health Coverage Exemptions (and instructions for figuring your shared responsibility payment):

Checkbox on Form 1040. The “Full-year coverage” checkbox that was on line 61 of the 2017 Form 1040 has been moved to page 1 of the 2018 Form 1040 and retitled “Full-year health care coverage or exempt.” You will now check that box if you, your spouse (if filing jointly), and anyone you can or do claim as a dependent had qualifying health care coverage or a coverage exemption that covered all of 2018 or a combination of qualifying health care coverage and coverage exemptions for every month of 2018. If you can check the box on Form 1040, you don’t need to file Form 8965.

Who Must File

• You are filing a Form 1040 (even if you are filing it because you are a dual-status alien for your first year of U.S. residency or a nonresident or dual-status alien who elected to file a joint return with a U.S. spouse),
• You can't be claimed as a dependent by another taxpayer,
• For one or more months of 2018, you or someone else in your tax household didn't have minimum essential coverage or a coverage exemption, and
• You can claim any part-year exemptions or exemptions for specific members of your tax household. This will reduce the amount of your shared responsibility payment. Attach Form 8965 to Form 1040.

Attach Form 8965 to your tax return.

TIP: Form 8965 is used only to claim and report coverage exemptions. If you are unable to check the “Full-year health care coverage or exempt” box on Form 1040, you don’t need to report the months when you and other members of your tax household had minimum essential coverage on Form 8965, but you may need to report a shared responsibility payment on your Form 1040. First check to see if you’re eligible for any coverage exemptions for some or all of the months that you or a member of your tax household weren’t covered.

Not required to file a tax return. If you aren't required to file a tax return, your tax household is exempt from the shared responsibility payment and you don't need to file a tax return to claim the coverage exemption. However, if you aren't required to file a tax return but choose to file anyway, you can check the “Full-year health care coverage or exempt” box on Form 1040. You don’t have to file Form 8965. (See the instructions under Part II, later, to see if your household or gross income is below the filing threshold.) 

Form 1040NR and Form 1040NR-EZ filers. If you file a Form 1040NR or Form 1040NR-EZ (including a dual-status tax return for your last year of U.S. residency) or someone claims you as a dependent on a Form 1040NR or Form 1040NR-EZ, you are exempt from the shared responsibility payment. Don't attach Form 8965 to your Form 1040NR or Form 1040NR-EZ.

For more information see chapters 1 and 6 of Pub. 519.

CAUTION! Only one Form 8965 should be filed for each tax household. If you can be claimed as a dependent by another taxpayer, you don't need to file Form 8965 and don't owe a shared responsibility payment.