The development of cost-effective electrical packaging for randomly distributed micro/nano-scale devices is a widely recognized challenge for fabrication technologies. Three-dimensional direct laser writing (DLW) has been proposed as a solution to this challenge, and has enabled the creation of rapid and low resistance graphitic wires within commercial polyimide substrates. In this work, we utilize the DLW technique to electrically contact three fully encapsulated and randomly positioned light-emitting diodes (LEDs) in a one-step process. The resolution of the contacts is in the order of 20μm, with an average circuit resistance of 29±18kΩ per LED contacted. The speed and simplicity of this technique is promising to meet the needs of future microelectronics and device packaging.