To check your e-file status, sign in to TurboTax, and go to Tax Home (if you're not already there). If you've submitted your return, you'll see a pending, rejected, or accepted status. If you haven't submitted your return yet, you'll see Let's keep working on your taxes! and sections like Personal Info and Income & Expenses.
Your e-file status is different from your refund status. If you want to track your refund, go to Where's My Refund.