It is not necessary to enclose a personal statement with a CV – but you might like to attach a cover letter instead. Just introduce yourself, and refer to your CV (e.g. “As you can see from my CV, my skills in (skill) and my educational background in (subject) make me an excellent candidate for this vacancy, as per the job description.”)
Another tip I learned in college was, start your CV with an 'About Me' or 'Personal profile'. It should be a complex sentence just saying who you are and what you are about. I learned this format:
“I am a (adjective, adjective) individual with a passion for/keen interest in (choose one), seeking employment as (job title).”
Short, sweet, and concise!