In this work we experiment with the hypothesis that words subjects use can be used to predict their psychological attachment style (secure, fearful, dismissing, preoccupied) as defined by Bartholomew and Horowitz. In order to verify this hypothesis, we collected a series of autobiographic texts written by a set of 202 participants. Additionally, a psychological instrument (Frías questionnaire) was applied to these same participants to measure their attachment style. We identified characteristic patterns for each style of attachment by means of two approaches: (1) mapping words into a word space model composed of unigrams, bigrams and/or trigrams on which different classifiers were trained (Naïve Bayes (NB), Bernoulli NB, Multinomial NB, Multilayer Perceptrons); and (2) using a word-embedding based representation and a neural network architecture based on different units (LSTM, Gated Recurrent Units (GRU) and Bilateral GRUs). We obtained the best accuracy of 0.4079 for the first approach by using a Boolean Multinomial NB on unigrams, bigrams and trigrams altogether, and an accuracy of 0.4031 for the second approach using Bilateral GRUs.