Can I start a Liquor distribution business?

Hello,
I am assuming that you are proposing a model where you purchase, stock and deliver liquor, and not a pure pick up and drop service.
While such a business is not expressly prohibited in law, its permissibly is a grey area. You will require a number of clearances and licenses for the same. For instance, you will require a license from the Commissioner appointed by the State Government under the provisions of the Karnataka Prohibition Act 1961, a license from the State Government under the Karnataka Excise (Sale of Indian and Foreign Liquors) Rules, 1968, permission for transportation of liquor under the Karnataka Excise (Possession Transport etc) Rules 1967 and certain other specific licenses.

no, it is illegal to transport liquor, however it is legal to sell liquor but not deliver or transport personally.

To transport liquor from distributor to wine store is allowed but not to resident houses