An electrical connector (50) comprises a housing (54b) provided with socket holes (52) for the reception of connector pins of a mating connector. A shutter (58) is provided linearly movable between a first end position, in which it covers socket holes, and a second end position, in which no socket holes are covered. Biasing means (60) are adapted to bias the shutter towards the first end position thereof. By providing the biasing means as at least one torsion spring (60)) having a first leg (60a) and a second leg (60b) interconnected by a helical spring portion (60c), very small dimension of the connector can be achieved.