"imposes responsibility" is correct and can be used in written English.
You can use it to describe when something or someone causes a person to have to be accountable for their actions. For example, "The new law imposed responsibility on employers to provide health insurance for their employees."
We hold freedom of speech dear, but accept that it imposes responsibilities of the sort that Savage is obviously not stable enough to understand.
Basic ideas have changed little, other than the fact that some modern statutes have imposed responsibility without fault and that corporations can now be held responsible for the acts of their management.
"Politicians don't seem to realise that the more you impose responsibility on schools the more they need that support.
An overall conflict surfaces between individual agents assuming responsibility for 'stewarding' bacteria, against funding systems and structures imposing responsibility for economic growth.
The entire raft of EU asylum law – from the Dublin regulation imposing responsibility for asylum, to the various directives setting out requirements for adequate treatment, due process, standard of living and international protection – is designed to reduce inconsistencies between member states so as to prevent forum shopping or "secondary movement" by asylum seekers.
It is true that sometimes the purpose of legal prohibition may be the simple one of imposing responsibility for the harm caused by a breach of that prohibition.
But Mr Justice Macduff decided the professional relationship between a priest and his bishop was sufficiently close so as to impose responsibility.
The settlement requires an academic institution, for the first time, to adopt the safety management model long prevalent in industry research, where lab safety is a well-recognized and legally imposed responsibility of leadership, enforced in organizations from the top down.
Do they need or even want that which they are fighting over or are they just fighting for some arbitrarily granted "right" or imposed "responsibility?" It is the responsibility and obligation of the bar to remind the citizens of our democracy that the price of liberty is eternal vigilance.
"I think this is clear from the attacks that are made not just on our court but even on national courts, where they take a decision which is unpopular: the problem is always seen in terms of the Human Rights Act which grants rights but doesn't actually impose responsibilities on the individual.
