Native English speakers, please.Is this sentence correct?

Since the satisfaction of the police precedes the filing of the case, the following may be considered.

If the police had not been satisfied that the witnesses were telling the truth, they would not have started a case against the accused.

Variants:

Only because the police were satisfied that the witnesses were telling the truth, they started a case against the accused.

The police started a case against the accused only because they were satisfied that the witnesses were telling the truth.

Your question is if the sentence is *correct*, and it is.

The others suggest you use "witnesses were" instead of "witnesses are", because this sounds slightly better.

But there is nothing wrong with "are". "If the police weren't" is not necessarily in the past - it is the subjunctive mood which is normal after "if".

In the moment that the speaker is saying the phrase, the police have already started the case, but they are still satisfied, and the witnesses are still presumably telling the truth.

Therefore, either "are" or "were" is fine.

You made one mistake. In the first half of your sentence, you start off in the past tense with "weren't", then switch to the present tense with "are", so I'd change it to:

If the police weren't satisfied that the witnesses were telling the truth, they wouldn't have started a case against the accused.

Other than that, it looks good.

....that the witnesses WERE telling the truth...