Are hormone levels the only tests for perimenopause?

NO Not Accurate. Hormone testing if abnormal is indicative of perimenopause, but normal levels may not be accurate. I've tested people, who are close to menopause and had results consistent with a 20 year old one month followed by those of 55 year old the next month. Hormone testing is very inaccurate. Symptoms are the most important factor with shortened and irregular cycles (<26 days).
Menopause. Pituitary levels of FSH LH can be checked as well.
FSH and LH. Are more accurate especially FSH in determining menopause.