Form 3582 is for e-filed returns only. The title at the top of the form is "Payment Voucher for Individual e-filed Returns CALIFORNIA FORM 3582 (e-file)." At the bottom of the form is the warning "Do not mail a paper copy of your tax
return with this payment voucher."
Furthermore, the Form 3582
instructions say, "Use form FTB 3582, Payment Voucher for Individual e-filed Returns, ONLY if BOTH of the following apply: 1) You filed your tax return electronically AND
2) You have a balance due and pay with a check or money order."
The Form 540 instructions for mailing your return say to include your payment, followed by your Form 540 return, followed by a copy of your federal return. There's not one little word about including a payment voucher.
If the FTB wanted you to use a payment voucher with your Form 540 paper return, wouldn't they call it "Form 540-V"?
