Overview.
With both the AstraZeneca and Johnson & Johnson (J&J)vaccines, there are multiple reports involving extremely rare clotting, including a type of blood clot called cerebral venous sinus thrombosis (CVST), that was seen in combination with low levels of blood platelets, called thrombocytopenia.

On April 9 2021 the ISTH released a report regarding indications of blood clots associated with the AstraZeneca Vaccine. A cascading number of European countries — including Germany, France, Italy, and Spain — suspended use of AstraZeneca’s COVID-19 vaccine https://www.isth.org/news/559981/
On April 12, 2021, the CDC created a Health alert about Cases of Cerebral Venous Sinus Thrombosis with Thrombocytopenia after Receipt of the Johnson & Johnson COVID-19 Vaccine.
Currently, the administration of the vaccine is in pause within the United States until further clarifications are found. CDC recommendations for Public Health includes the following: