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Simple Summary: Cutaneous melanoma (CM) is an aggressive skin cancer that develops from melanocytic cells. The most important prognostic factor is still the vertical tumour thickness according to Breslow. Liver function is associated with better overall patient outcomes and is currently under increasing investigation in cancer patients. Current findings show that liver function is an important factor in different tumour entities and represents a potential biomarker. Therefore, we aimed to evaluate liver metabolism by using liver scores in CM. High tumour thickness (≥1.66 mm) and aspartate transaminase-to-platelet ratio index (APRI ≥ 0.2241) at the initial diagnosis were associated with a worse prognosis in stage I and II melanoma. Background: Neoadjuvant and adjuvant therapies are currently getting increasingly important in cutaneous melanoma (CM) management. However, there is still a lack of prognostic tools to identify which patients have a poor prognosis. There is increasing evidence that the liver score may be a potential prognostic parameter in different tumour types. The aim was to investigate whether established liver scores can establish the prognosis of CM. Methods: According to established methods, the APRI, the MELD score, the MELD-Na score and the De Ritis ratio were calculated from the laboratory values at the time of the initial diagnosis. Survival was compared with the Kaplan–Meier curve and tested with log-rank tests. Risk factors associated with cutaneous melanoma-specific survival (CMSS) and progression-free survival (PFS) were assessed by using the Cox proportional hazards regression model. To determine the diagnostic accuracy, we performed a time-dependent ROC analysis. Results: A total of 423 patients were included, including 141 patients in AJCC stage (2017) I (33.3%), 82 in stage II (19.4%), 128 in stage III (30.3%) and 72 in stage IV (17%). Median time until melanoma-specific death was 99 months (IQR: 37–126). In addition, 37.6% of patients relapsed with a median time to relapse of 88 months (IQR: 17.5–126). In all stages, tumour thickness and ulceration were independent markers for predicting CMSS and PFS (p < 0.05). The multivariable analysis with all stages showed no significant association with CM outcome for liver scores (p > 0.05). The subgroup analysis revealed that the APRI (≥0.2241) was associated with CMSS and PFS in melanoma stages I and II, independently of tumour thickness, age and ulceration (HR 2.57, 95% CI 1.14–5.75; HR 2.94, 95% CI 1.42–6.09, respectively). Conclusions: The 20-year prognosis of AJCC stage I and II CM was dependent on tumour thickness and the APRI. High tumour thickness and an APRI ≥ 0.2241 at the initial diagnosis were associated with a worse prognosis. Future studies should investigate the independent prognostic value of the APRI in low-stage CM. Furthermore, the APRI score could be a potential biomarker for nomograms. [ABSTRACT FROM AUTHOR]