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A friend of mine is suing someone. I (and others) witnessed all of the violations that are claimed, but I'm unable to attend the hearing in person for various reasons (mainly that I've moved out of state).

I'm writing a statement for my friend to present in the case, and wasn't sure how to address it. My plan was to use

To Whom It May Concern

or

To All Interested Parties:

or

To the court

or

Dear <Judge's Name>,

or

Your honor, complainants, respondents, and witnesses:

But I don't know that any of these are considered appropriate. Most likely I will choose the first.

What is the standard form of address in written statements to be presented during civil proceedings? Also, who is actually being addressed here?

As the answer by Iñaki Viggers says, you should submit an affidavit, not simply a letter to the court. An unsworn letter will probably not be admissible at all.

It is common for a witness to tell his or her story to the lawyer for the side that wishes to use the affidavit, and for the lawyer to then draft the actual affidavit in such a way that it will be acceptable to the court where it will be used. Then the lawyer sends it to the affiant (the person who would be a witness if s/he came to court, who is making the affidavit) with instructions. Generally an affidavit must be notarized or otherwise sworn to in front of an appropriate official.

However, a person can draft his or her own affidavit. It is usual for it to be headed with the name and case number of the case where it will be used. It should include a statement that everything in it is true, and that the affiant swears (or affirms) this under penalty of perjury. It should include only relevant facts that the affiant has personally witnessed, not anything heard from anyone else, or guessed at or deduced.

The facts should be stated clearly and simply.

The affidavit should be signed in the presence of a notary, who will witness the signature and the oath that the contents are true.

This WikiHow page describes the process in detail, with a template form.

How should I address a statement to be presented as evidence in a civil case?

The way of addressing the readers is irrelevant. What matters is that the statements your affidavit (which is what you really should produce) be concise and unequivocal so that it is not discarded for purposes of fact-finding.

Your affidavit will (or at least it should) be read by the judge, the jury, all parties/lawyers in the case, and (if the ruling of the case is appealed) judges in upper courts. Witnesses and other non-parties are also likely to read your testimony. In fact, you can only expect the defendant(s) through counsel(s) will dispute your credibility in their attempt to impeach/strike your testimony.