Transcranial direct current stimulation (tDCS) provides a means of non-invasively inducing plasticity-related changes in neural circuits in vivo and is experiencing increasing use as a potential tool for modulating brain function. There is growing evidence that tDCS-related outcomes are likely to be influenced by an individual's brain state at the time of stimulation, i.e., effects show a degree of 'state-dependency'. However, few studies have examined the behavioural and physiological impact of state-dependency within cognitively salient brain regions. Here, we applied High-Definition tDCS (HD-tDCS) over the left dorsolateral prefrontal cortex (DLPFC) in 20 healthy participants, whilst they either remained at rest, or performed a cognitive task engaging working memory (WM). In a third condition sham stimulation was administered during task performance. Neurophysiological changes were probed using TMS-evoked potentials (TEPs), event-related potentials (ERPs) recorded during n-back WM tasks, and via resting-state EEG (RS-EEG). From a physiological perspective, our results indicate a degree of neuromodulation following HD-tDCS, regardless of task engagement, as evidenced by changes in TEP amplitudes following both active stimulation conditions. Changes in ERP (P3) amplitudes were also observed for the 2-Back task following stimulation delivered during task performance only. However, no changes were seen on RS-EEG for any condition, nor were any group-level effects of either stimulation condition observed on n-back performance. As such, these findings paint a complex picture of neural and behavioural responses to prefrontal stimulation in healthy subjects and provide only limited support for state-dependent effects of HD-tDCS over the DLPFC overall.