No, you don’t need an opposite house prime sponsor when your bill is introduced.  You must, however, have an opposite house prime sponsor before your bill can pass on third reading in the house in which you serve.  So, before your bill is heard on third reading, talk with a member of the opposite house about being the second-house prime sponsor on your bill.  Once someone agrees, talk to the Chief Clerk of the House if you’re a representative, or to the Secretary of the Senate if you’re a senator, about the form you need to fill out.  After you turn the form in to the front desk of the house in which you serve, the front-desk staff will make sure that the opposite house prime sponsor’s name appears on the reengrossed version of your bill when it is introduced in the second house.