“书面声明”常见的英文表达是 “written statement” 。
例句：
The witness needs to provide a written statement about what he saw at the scene. （目击者需要就他在现场所看到的情况提供一份书面声明。）
We require a written statement from your company regarding this matter. （我们要求贵公司就此事提供一份书面声明。）