What is the ruling on signing a declaration that proves the innocence of an accused person, knowing that the signatory did not testify before the judge, and that the accused is indeed innocent?

The basic rule regarding lying and bearing false witness is that they are forbidden, unless a major benefit, greater than the lie, results from them, such as the allowance to save an innocent person from imprisonment. This allowance is for necessity if it is the only way to reach the truth and the use of allusions (ta'areedh) is not possible.