When do we use: File with and file at

[Hellohello]

For instance, I want an agency or company to receive my documents. Do you say, file with or file at?

[Mister Micawber]

Neither, I think. Please supply a complete sentence.
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Native English teacher at Mister Micawber's

[Hellohello]

For example: This document should be filed with the State Department. Is this correct? On the other hand, can you say: This document should be filed at the State Department? Is this also correct?

[Mister Micawber]

OK-- either will work. 'With' seems better to me.
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Native English teacher at Mister Micawber's

[Milanya]

...filed with an organization, ...sent to an organization
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con·text - The part of a text or statement that surrounds a particular word or passage and determines its meaning.