Laser-based fabrication of metal-halide perovskite mini-modules has recently been demonstrated using nanosecond (ns) laser pulses. However, it still suffers from high-resistance contacts due to remaining PbI2 residues at the bottom of the absorber-opening P2 scribe line. Therefore, in this study, we investigate the effect of shorter picosecond (ps) laser pulses, and thus lower heat input, on the complete removal of perovskite during P2 laser patterning to achieve low series resistances and thus improved electrical performances. Based on a systematic variation of the incident laser fluence and a comprehensive electrical, morphological and compositional analysis of the scribed area, optimal process windows for successful laser-based series interconnection are identified and evidenced by current density-voltage curves. The amount of PbI2 debris at the scribe bottom is reduced by using ps instead of ns pulses, resulting in improved j-V performance due to higher fill factor and lower series resistance. A numerical analysis of the laser-induced depth-dependent temperature profile shows that overcritical heating for both pulse durations induces explosive boiling of the excited volume, but only in the case of ns structuring the melting point of the underlying transparent oxide contact layer is exceeded. The corresponding scribed line morphology shows features of thermally-driven direct ablation (i.e., splashes), whereas ps pulses produce scribe lines with steep walls and delaminated areas, indicating a mechanical stress-assisted lift-off ablation. Accordingly, P2 laser patterning with ps pulses is recommended due to favorable morphological (steep edges) as well as composition-related (less PbI2 residues) scribe line properties.