The phrase "a formal responsibility" is correct and usable in written English.
You can use it when referring to a duty or obligation that is officially recognized or required in a professional or organizational context.
Example: "As the project manager, I have a formal responsibility to ensure that all deadlines are met and that the team is supported."
Alternatives: "an official duty" or "a designated obligation".
Perhaps the auditing function should also have a formal responsibility to customers, as well as to shareholders.
Supervisors have a formal responsibility for helping their research students develop the understandings and skills required for undertaking research.
The driver was in a position to lead the audit process - "Whoever is in charge - it must be a formal responsibility" [DS1-S2-GA].
However, since they were not in faculty positions for which teaching was a formal responsibility and part of annual evaluations, their interest and willingness to implement transformed teaching was perhaps less constrained by traditional departmental expectations.
This has been an area of formal responsibility for the project's General Contractor, the Pacific International Center for High Technology Research PICHTRR) based in Honolulu.
The Board is a national authority with formal responsibility for decision-making for changes in local traffic regulations, i.e. specifically with regard to deviations from the "base level speed limit" on specific stretches of road, often in response to requests from private persons to lower the existing speed limits (e.g. on roads in direct proximity to areas with children at play).
As the prescription of medicines forms just one element in the medical care of a patient, formal responsibilities are also established for the related tasks in the treatment process, viz.
But in 2003 it underwent a dramatic rehabilitation by taking formal responsibility for the bombing, paying compensation and handing over two Libyan suspects, one of whom, Abdelbaset Ali al-Megrahi, was convicted for the attack.
It is not always clear, and certainly rarely put in writing, who has formal responsibility for a child – it is not necessarily the biological parent.
Formal responsibility for H&S within a large organization is that of a manager trained to ensure that policies of the company and legal requirements are adhered to by the supervisory organization.
At each level of local government, a People's Assembly, composed of representatives elected by popular vote, chooses a People's Committee that has formal responsibility within the locality for public administration and security.
