No, there is no formal written test to acquire the multi-engine rating. You will do a certain number of hours of training and then you’ll be tested through an oral exam and a flight check with an authorized flight examiner. You should try and revise the recommended material leading up to your oral exam, as the examiner may ask some tricky questions that may not be so much to do with practical training. You will not have to take another FAA written test like you did when you were getting your pilot’s license.