No, you do not need to connect any power connectors to this card.
"Slide the card into a free PCIe 8x / 16x slot and connect a monitor. You can now power up the PC. Once Windows boots up, install the latest Catalyst drivers and make sure your operating system is fully patched up, especially DirectX. After driver installation, reboot the PC and you are ready to go." -installation part of Guru3D review of the card.