You're probably thinking of the manifest required under 14 CFR 135.61(c). This only applies to multi engine airplanes, however.
You are still bound by 91.103, which requires that prior to beginning a flight, the PIC shall become familiar with all information regarding that flight.
You are not required to have a completed weight and balance form on board. However, it's a good idea to be able to show how you determined your airplane, as loaded, is in compliance. Accordingly, you may keep a calculation showing the same load, if you use it regularly, or you may calculate it every time.
I know an individual who was ramped while flying a single engine airpane. The inspector demanded a completed weight and balance for the load. The individual excused himself for a trip to the restroom, and returned several minutes later with the weight and balance written on a length of toilet paper. He instructed the inspector to flush it when he was done, and departed with passengers and cargo. I don't recommend this, but it worked.
