Background: Pulmonary tuberculosis (PTB) remains a major public health concern globally and continues to cause substantial morbidity and mortality, particularly in resource-limited settings. Early detection among presumptive TB cases is critical for timely treatment initiation and reducing transmission. Methods: A hospital-based cross-sectional study was conducted from April to August 2025 at Akim Oda Government Hospital. A total of 234 participants aged 10–40 years with symptoms suggestive of PTB (especially cough ≥2 weeks) were recruited using a purposive sampling technique. Sputum samples were collected and analyzed using Ziehl–Neelsen smear microscopy and GeneXpert MTB/RIF assay for detection of Mycobacterium tuberculosis. A structured questionnaire was administered to obtain socio-demographic characteristics and risk factor information. Data were analyzed using SPSS version 26, and associations between PTB status and selected variables were tested using Chi-square, with statistical significance set at p < 0.05. Results: Out of the 234 participants, 50 tested positive, giving an overall PTB prevalence of 21.4% (50/234). GeneXpert detected PTB in 26.6% (24/90) of tested samples, while smear microscopy detected PTB in 18.1% (26/144). PTB positivity was significantly associated with age group (p = 0.001) and gender (p = 0.019), with the highest burden observed among participants aged 30–40 years and among males. Sputum appearance was significantly associated with PTB detection by both GeneXpert (p = 0.014) and microscopy (p = 0.020), with mucopurulent samples yielding the highest positivity. Among the risk factors assessed (smoking, alcoholism, family history, overcrowding, and malnutrition), none showed significant association with PTB positivity (p > 0.05); however, TB awareness demonstrated a borderline association (p = 0.067). Conclusion: Pulmonary tuberculosis prevalence among presumptive TB patients at Akim Oda Government Hospital was high (21.4%). GeneXpert MTB/RIF demonstrated a higher detection yield than smear microscopy. Age, gender, and sputum quality were significant predictors of PTB positivity, emphasizing the need for strengthened facility-based screening, improved sputum collection practices, and expanded access to rapid molecular diagnostics.