Would the family be suing for damages if there was no death certificate. Bear in mind, it takes 30 days or more to even get a death certificate.
Family readies lawsuit against Capitol Police officer who fatally shot rioter
https://www.washingtontimes.com/news/2021/may/20/family-ashli-babbitt-lawsuit-capitol-police/
The Washington Times is a very reliable source.
There are some FReepers who prefer the WaPo to a conservative blogger posting.