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

Who Must File
File Form 8965 to report or claim a coverage exemption if all of the following apply:

• You are filing a Form 1040, 1040A, or 1040EZ (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 2017, you or someone else in your tax household didn't have minimum essential coverage, and
• You want to report or claim a coverage exemption for yourself or another member of your tax household.

Attach Form 8965 to your tax return (Form 1040, Form 1040A, or Form 1040EZ).

TIP: Form 8965 is used only to claim and report coverage exemptions. If you are unable to check the Full-year coverage box on your tax return, 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, 1040A, or 1040EZ. 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 must claim the coverage exemption on line 7 of Form 8965. (See the instructions under Part II, later.)

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 a personal exemption deduction for you 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.