BERLIN—Tesla has withdrawn its application for state funding for its planned battery factory near Berlin, the electric vehicle maker said on Friday, adding that construction plans were unchanged. The European Union in January approved a plan that included giving state aid to Tesla, BMW, and others to support production of electric vehicle batteries and help the bloc to reduce imports from industry leader China. Tesla was expected to receive 1.14 billion euros ($1.28 billion) in EU funding for its battery plant in Gruenheide, Brandenburg under the plan, with a final decision likely by the end of the year. The U.S. carmaker did not say why it had withdrawn its application for funding. The company is itself investing 5 billion euros in the battery plant, according to German economy ministry estimates. Meanwhile, construction of a car production site alongside the battery plant, which Tesla has begun building under pre-approval permits while …