Absolutely yes, a person can have both a personal loan and a home loan. If you had taken a personal loan earlier and are looking for a home loan, banks do offer you the home loan provided your debt to income ratio is not above 50%.
If the EMI outgo on both the loans does not cross 50% of your income, the banks are ready to lend to you. In case your home loan eats up majority of your income, it might become difficult to get another loan. Hence the lenders check your repaying ability and current credit rating.