Inverter circuits have been made by connecting two high-quality pentacene field-effect transistors. A uniform and pinhole-free 900 nm thick polyimide gate-insulating layer was formed on a flexible polyimide film with gold gate electrodes and partially removed by using a CO2 laser drilling machine to make via holes and contact holes. Subsequent evaporation of the gold layer results in good electrical connection with a gold gate layer underneath the gate-insulating layer. By optimization of the settings of the CO2 laser drilling machine, contact resistance can be reduced to as low as 3 ohms for 180 microm square electrodes. No degradation of the transport properties of the organic transistors was observed after the laser-drilling process. This study demonstrates the feasibility of using the laser drilling process for implementation of organic transistors in integrated circuits on flexible polymer films.