Resting state fMRI (rs-fMRI) provides imaging biomarkers of task-independent brain function that can be associated with clinical variables or modulated by interventions such as behavioral training or pharmacological manipulations. These biomarkers include time-averaged regional brain function as manifested by regional cerebral blood flow (CBF) measured using arterial spin labeled (ASL) perfusion MRI and correlated temporal fluctuations of function across brain networks with either ASL or blood oxygenation level dependent (BOLD) fMRI. Resting-state studies are typically carried out using just one of several prescribed state conditions such as eyes closed (EC), eyes open (EO), or visual fixation on a cross-hair (FIX), which may affect the reliability and specificity of rs-fMRI. In this study, we collected test-retest ASL MRI data during 4 resting-state task conditions: EC, EO, FIX and PVT (low-frequency psychomotor vigilance task), and examined the effects of these task conditions on reliability and reproducibility as well as trait specificity of regional brain function. We also acquired resting-state BOLD fMRI under FIX and compared the network connectivity reliabilities between the four ASL conditions and the BOLD FIX condition. For resting-state ASL data, EC provided the highest CBF reliability, reproducibility, trait specificity, and network connectivity reliability, followed by EO, while FIX was lowest on all of these measures. PVT demonstrated lower CBF reliability, reproducibility and trait specificity than EO and EC. Overall network connectivity reliability was comparable between ASL and BOLD. Our findings confirm ASL CBF as a reliable, stable, and consistent measure of resting-state regional brain function and support the use of EC or EO over FIX and PVT as the resting-state condition.