Attachment styles are known to have significant associations with mental and physical health. Specifically, insecure attachment leads individuals to higher risk of suffering from mental disorders and chronic diseases. The aim of this study is to develop an attachment recognition model that can distinguish between secure and insecure attachment styles from voice recordings, exploring the importance of acoustic features while also evaluating gender differences. A total of 199 participants recorded their responses to four open questions intended to trigger their attachment system using a web-based interrogation system. The recordings were processed to obtain the standard acoustic feature set eGeMAPS, and recursive feature elimination was applied to select the relevant features. Different supervised machine learning models were trained to recognize attachment styles using both gender-dependent and gender-independent approaches. The gender-independent model achieved a test accuracy of 58.88%, whereas the gender-dependent models obtained 63.88% and 83.63% test accuracy for women and men respectively, indicating a strong influence of gender on attachment style recognition and the need to consider them separately in further studies. These results also demonstrate the potential of acoustic properties for remote assessment of attachment style, enabling fast and objective identification of this health risk factor, and thus supporting the implementation of large-scale mobile screening systems.