It does apply to federal extensions too, you'll see that Form 4868 has a spot for your SSN (Box 2) and a spot for your partner/spouse (Box 3).
<a rel="nofollow" target="_blank" href="
https://www.irs.gov/pub/irs-pdf/f4868.pdf">https://www.irs.gov/pub/irs-pdf/f4868.pdf</a>
