I'd like to look into this, but none of the websites that report on this appear to be giving their source. Can you point me to the court case name / reference / plaintiff vs defendant?

Edit 1:

Nevermind I found it :

Case # 19-cv-11947-LJL
"INSTITUTE FOR AUTISM SCIENCE and INFORMED CONSENT ACTION NETWORK vs CENTERS FOR DISEASE CONTROL AND PREVENTION"

Edit 2:

Ok, checked the details, the interpretation is a little bit hyperbolic here.

CDC didn't "admit in Federal Court that they have no evidence 'vaccines don’t cause autism'". That's not what happened. What actually happened is that CDC submitted a list of studies in response to the plaintiff's FOIA that requested all evidence the CDC had that vaccines didn't cause autism, and in retrospect upon checking the studies submitted by the CDC, it appears that although some of the studies provided by the CDC did indeed support the idea of an absence of correlation between the use of certain vaccines / ingredients in isolation and the onset of autism, none of the studies the CDC provided in reply to the FOIA support the claim that

• the DTaP vaccine (specifically) doesn't cause autism
• the combination of several vaccines doesn't cause autism
• the use of vaccines in children 6 months and younger doesn't cause autism

In other words, this court proceeding proves either of two things:

• the CDC omitted some studies from the FOIA, or
• the CDC only has evidence that "Vaccines X, Y and Z - taken in isolation - do not appear to cause autism in children 6 months and aboves based on statistical evidence" and was therefore being misleading and unscientific when making the much more general claim that "Vaccines do not cause autism" for which they do not have sufficient evidence.

So no the CDC didn't "admit that they have no evidence that 'vaccines don't case autism'". They actually showed that they had some evidence that some vaccines used in isolation do not apparently cause autism in children 6 months and higher. But the failure to provide sufficient evidence to back the wilder and much more general claim that "vaccines (in general) don't cause autism (in any case whatsoever)" can be legally interpreted as either a failure to comply to the FOIA (and therefore an offense under the same act), or an implicit admission that the more general claim was unscientific and therefore unfounded.