No particular "degree" from a school or college is required for entry into the industry, and there is no "certification" for most parts of the industry.
But what is important are the skills you bring to the table when you enter the business and want to move up. For instance, if you want to work as an assistant to a composer or songwriter, a thorough understanding of the industry and how the composing or songwriting process works is important. Also important can be the technical skills you have (such as knowledge and experience with Pro Tools software, computers, and other technology) as this may prove very valuable to a prospective employer.
Your skills also come into play when you want to be hired by an independent filmmaker to write music for his/her film... if you can provide technical information and resources about music and sound for film, your usefulness and value to the filmmaker can be greatly increased.