We have investigated the distribution of measured heights of single CdSe colloidal quantum dots (QDs) by contact-mode atomic force microscopy. The dot heights measured with metal-coated Si tips, with which large adhesive force is measured between the tip and sample, are much smaller than that expected from optical absorption. This discrepancy could be due to the dot position fluctuation that occurs when the tip is in contact with the dot because the height distribution of the QDs covered with very thin SiO2 layer is in agreement with the optical measurement. On the other hand, when conductive carbon nano-tube (CNT) tips are used, the adhesive force is reduced significantly, and the measured dot heights become close to the expected value. Thus, the measurement of QD height is greatly improved in accuracy with CNT tips. As a result, the current flowing through the QD can be measured, and conductance changes attributed to electron resonant tunneling through the QD are observed.