No, you don't need the visa. Just let the airlines know that you have both passports and can access each country. If you do it like I previously stated, none of the country border officials will need to see a visa either. If you have a valid Ghanaian passport, you shouldn't need a visa to enter or exit Ghana. Make sure that your passport isn't expired. If it is, you will need to renew it with the consulates.
The dual citizen card is incredibly hard to acquire. I tried to apply years ago and learned they hardly issue it.