Crime activity in many cities worldwide causes significant damages to the lives of victims and their surrounding communities. It is a public disorder problem, and big cities experience large amounts of crime events. Spatio-temporal prediction of crimes activity can help the cities to have a better allocation of police resources and surveillance. Deep learning techniques are considered efficient tools to predict future events analyzing the behavior of past ones; however, they are not usually applied to crime event prediction using a spatio-temporal approach. In this paper, a Convolutional Neural Network (CNN) together with a Long-Short Term Memory (LSTM) network (thus CLSTM-NN) are proposed to predict the presence of crime events over the city of Baltimore (USA). In particular, matrices of past crime events are used as input to a CLSTM-NN to predict the presence of at least one event in future days. The model is implemented on two types of events: "street robbery" and "larceny". The proposed procedure is able to take into account spatial and temporal correlations present in the past data to improve future prediction. The prediction performance of the proposed neural network is assessed under a number of controlled plausible scenarios, using some standard metrics (Accuracy, AUC-ROC, and AUC-PR).