We investigate tunneling through a resonant level formed in a carbon nanotube quantum dot contacted by resistive metal wires. These contacts create a dissipative environment for the electrons tunneling across the nanotube, thus suppressing the tunneling rate. We study the shape of the resonant peak in the nanotube conductance, with the expectation that the peak width and height, both dependent on the tunneling rate, will be suppressed. Instead, we find that the behavior crucially depends on the ratio of the tunneling rates from the resonant level to the two contacts. We discuss the implication of our findings for a boundary quantum phase transition in this system. © Published under licence by IOP Publishing Ltd.