The phrase "assess responsibilities" is correct and usable in written English.
You can use it when evaluating or analyzing the duties and obligations assigned to individuals or groups in a specific context.
Example: "In our meeting, we will assess responsibilities to ensure everyone understands their roles in the project."
Alternatives: "evaluate duties" or "review obligations".
Russian prosecutors said they would open a criminal investigation to assess responsibility for the environmental damage.
The authorities moved with unusual speed to assess responsibility for the accident.
If, indeed, it mattered, it would be impossible finally to assess responsibility for the ensuing fracas.
Gen. George W. Casey Jr., the Army chief of staff, ordered the inquiry to determine how Rolling Stone was granted access to a wartime commander and also to assess responsibility for quotations offensive to civilian leaders.
KABUL, Afghanistan — A commission appointed by President Hamid Karzai to assess responsibility for the massive fraud at Kabul Bank issued its report on Sunday, absolving the president's brother of any blame.
The commission, appointed by President Karzai to assess responsibility for the wide-ranging fraud scheme, said last month that 207 borrowers, including members of the president's cabinet and Parliament, had taken out undocumented loans.
On Sunday, a panel appointed by President Hamid Karzai to make recommendations and assess responsibility for large-scale fraud at the private bank had faulted the Central Bank as well as international auditors, financed by American aid money, for failing to uncover the deception sooner.
Of the total, 174 crashes had been attended by the police, who filled in a standardised form containing data that allowed us to assess responsibility by the same method.
And how, with so many of our witnesses, when it comes to assessing responsibility, all fingers point away from themselves.
Yet, in assessing responsibility, the commission pointed not to current students and administrators but to an insular university culture that for years had resisted change and discouraged criticism.
