Is there a test to show if I am in perimenopause?

No. The tests for menopause are very unreliable for perimenopause, perimenopause is better defined by the symptoms, which can last for months or years before periods stop completely. Sometimes, perimenopausal symptoms will come and go for a number of years before their final time.Especially, with this type of course, tests will be unreliable.
Your gyn can do. An fsh and lh test to see if those are becoming elevated but you usually go by your symptoms, please discuss with your gyn.