Can ovulation still happen in perimenopause?
Ask a clinician, and bring a few months of cycle dates so they can see your pattern. Until you have an answer, do not rely on a guess about ovulation for contraception. The public health pages linked below describe the transition in general.
Public pages on the transition
The FDA's menopause page and the Office on Women's Health menopause page describe the transition in general terms. The Menopause Society's sexual health pages are the one to open if your question is really about sex and contraception.
Tracking dates before you ask about birth control
Track your cycle dates for a few months, along with symptoms and any missed doses if you are on a plan. Bring the record to your next visit. Ask directly: given where I am, should I still be using birth control, and does my plan change?
Why a cycle record helps your clinician
Tracking your cycle alongside a therapy plan gives your clinician something concrete, and questions about ovulation, pregnancy risk and contraception belong with a licensed clinician.