Can I close the Apple account if I am an immediate family member of the deceased and I have a death certificate?

Yes. This section from Apple's legal documents addresses that very question:

Legal - iCloud - Apple

IV. D.

Upon receipt of a copy of a death certificate your Account may be terminated and all content within your Account deleted. Contact iCloud Support at iCloud - Official Apple Support for further assistance.

Sorry for the loss.

See -> How to request access to a deceased family member's Apple account

How to request access to a deceased family member's Apple account - Apple Support