If I am partial owner of a house, can I sell my half of the home?

Yes.  You have a legal right to sell your partial ownership interest in the house.  However, as a practical matter, the market for a half interest in a house has got to be extremely limited.  The number of people who would be interested in buying a partial ownership of a house with a stranger has to be extraordinarily small.  And the practical implication is that one would expect the market value for a partial interest in a piece of real estate to be highly impaired.  Such a transaction might work in a practical way if the two people own a piece of real estate as an investment, and both co-owners agreed to the substitution of a new investor for one of the two existing investors.  Essentially, the new person to the deal would become a partner with one of the original co-owners.  This could be a sale at a serious price for the half-interest; such as one-half of the fair market value of the entire parcel. 

Also, sometimes when two members of a family (siblings; parent and child; or some other combination) are co-owners of a piece of property, one of them may make a deal to sell his/her share to another family member.  This type of transaction is legal and can be a practical solution to a co-owner's desire to liquidate his/her share.  Such a transaction can result in a sale at a price that is mutually satisfactory to the buyer and seller.