True
The CDC changed course on April 3:
"The Coronavirus Crisis: CDC Now Recommends Americans Consider Wearing Cloth Face Coverings In Public", npr,org April 3, 20205:49 PM ET
On that day April 3 a webpage from the CDC went live called "Recommendation Regarding the Use of Cloth Face Coverings, Especially in Areas of Significant Community-Based Transmission" under the heading tab "Prevent Getting Sick". And it did not have a single reference to support its findings:

This is the entire text the public got to see on the web when the CDC made the recommendation on April 3:
CDC continues to study the spread and effects of the novel coronavirus across the United States. We now know from recent studies that a significant portion of individuals with coronavirus lack symptoms (“asymptomatic”) and that even those who eventually develop symptoms (“pre-symptomatic”) can transmit the virus to others before showing symptoms. This means that the virus can spread between people interacting in close proximity—for example, speaking, coughing, or sneezing—even if those people are not exhibiting symptoms. In light of this new evidence, CDC recommends wearing cloth face coverings in public settings where other social distancing measures are difficult to maintain (e.g., grocery stores and pharmacies) especially in areas of significant community-based transmission.
It is critical to emphasize that maintaining 6-feet social distancing remains important to slowing the spread of the virus. CDC is additionally advising the use of simple cloth face coverings to slow the spread of the virus and help people who may have the virus and do not know it from transmitting it to others. Cloth face coverings fashioned from household items or made at home from common materials at low cost can be used as an additional, voluntary public health measure.
The cloth face coverings recommended are not surgical masks or N-95 respirators. Those are critical supplies that must continue to be reserved for healthcare workers and other medical first responders, as recommended by current CDC guidance.
This recommendation complements and does not replace the President’s Coronavirus Guidelines for America, 30 Days to Slow the Spread, which remains the cornerstone of our national effort to slow the spread of the coronavirus. CDC will make additional recommendations as the evidence regarding appropriate public health measures continues to develop.
To be fair, while the claim is true that the CDC published a recommendation that did not have a single supporting study cited: Later they added some links to that page. Unfortunately, none of relevance to anyhow 'prove' cloth masks would offer any benefit — in fact, never ever even later than that on this constantly updated page to support their recommendations with reliable evidence. Only some scaremongering people into the belief that asymptomatic spread would be the main driver of spread. And only some that as per mechanistic plausibility would suggest that (mandated) masks in community settings would or could somehow 'help'.
On April 5 the CDC added the following references:
Recent Studies:
Rothe C, Schunk M, Sothmann P, et al. Transmission of 2019-nCoV Infection from an Asymptomatic Contact in Germany. The New England journal of medicine. 2020;382(10):970-971.
Zou L, Ruan F, Huang M, et al. SARS-CoV-2 Viral Load in Upper Respiratory Specimens of Infected Patients. The New England journal of medicine. 2020;382(12):1177-1179.
Pan X, Chen D, Xia Y, et al. Asymptomatic cases in a family cluster with SARS-CoV-2 infection. The Lancet Infectious diseases. 2020.
Bai Y, Yao L, Wei T, et al. Presumed Asymptomatic Carrier Transmission of COVID-19. Jama. 2020.
Kimball A HK, Arons M, et al. Asymptomatic and Presymptomatic SARS-CoV-2 Infections in Residents of a Long-Term Care Skilled Nursing Facility — King County, Washington, March 2020. MMWR Morbidity and mortality weekly report. 2020; ePub: 27 March 2020.
Wei WE LZ, Chiew CJ, Yong SE, Toh MP, Lee VJ. Presymptomatic Transmission of SARS-CoV-2 — Singapore, January 23–March 16, 2020. MMWR Morbidity and mortality weekly report. 2020;ePub: 1 April 2020.
Li R, Pei S, Chen B, et al. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2). Science (New York, NY). 2020.
As evidenced by those studies: None 'covering' any type of mask.
Of note is that the very first study cited by the CDC is of the same quality as the others of those quoted: 'dubious':
So, that paper we all reported on showing transmission of #2019nCoV from an “asymptomatic case”? Well, it turns out the woman did have symptoms. Here’s what we know so far:
Study claiming new coronavirus can be transmitted by people without symptoms was flawed
A traveler to Germany from China who infected another person did feel ill, contradicting New England Journal of Medicine report
— kakape (on Twitter 12:00 AM · Feb 4, 2020)
Highlighting his scoop published in Science:
— Kai Kupferschmidt: "Study claiming new coronavirus can be transmitted by people without symptoms was flawed", Science, Feb. 3, 2020 , 5:30 PM