A pressure sensor for detecting the pressure of a fluid, having a sensor body (2; 2') that comprises at least one first body part (3; 3') and one second body part (4; 4') each having a first face and a second face opposite to one another, wherein the first body part (3; 3') and the second body part (4; 4') are joined together in such a way that the first face of the first body part (3; 3') faces the first face of the second body part (4; 4'), at a distance therefrom; wherein at least one of the first body part (3; 3') and the second body part (4, 4') includes a membrane portion (7; 7'), subject to elastic flexure or deformation towards the other one of the first body part (3; 3') and the second body part (4; 4') as a result of pressure of the fluid, the membrane portion (7; 7') defining at least part of the first face of the first body part (3; 3') or of the second body part (4; 4'); wherein the pressure sensor has a circuit arrangement (8, 10) supported by the sensor body, which comprises at least one first electrical circuit that extends at least in part at the membrane portion (7; 7') and is configured at least for detecting one said elastic flexure or deformation through at least one respective detection component (R1, R2, R3, R4) in order to provide first information representative of a measurement of pressure; wherein the first electrical circuit is associated to the first face of one of the first body part (3; 3') and the second body part (4; 4'), and the first face of the other one of the first body part (3; 3') and the second body part (4; 4') forms or has associated thereto at least one circuit element, prearranged for interacting with the first electrical circuit when one said elastic flexure or deformation of the membrane portion (7; 7') is of a degree at least equal to a substantially predetermined limit, to generate thereby second information or signalling, the second information or signalling being representative of at least one from among an excessive pressure of the fluid, an incorrect pressure measurement, and an anomalous state of the pressure sensor. wherein the first body part (3; 3') and the second body part (4; 4') are joined together in such a way that the first face of the first body part (3; 3') faces the first face of the second body part (4; 4'), at a distance therefrom; wherein at least one of the first body part (3; 3') and the second body part (4, 4') includes a membrane portion (7; 7'), subject to elastic flexure or deformation towards the other one of the first body part (3; 3') and the second body part (4; 4') as a result of pressure of the fluid, the membrane portion (7; 7') defining at least part of the first face of the first body part (3; 3') or of the second body part (4; 4'); wherein the pressure sensor has a circuit arrangement (8, 10) supported by the sensor body, which comprises at least one first electrical circuit that extends at least in part at the membrane portion (7; 7') and is configured at least for detecting one said elastic flexure or deformation through at least one respective detection component (R1, R2, R3, R4) in order to provide first information representative of a measurement of pressure; wherein the first electrical circuit is associated to the first face of one of the first body part (3; 3') and the second body part (4; 4'), and the first face of the other one of the first body part (3; 3') and the second body part (4; 4') forms or has associated thereto at least one circuit element, prearranged for interacting with the first electrical circuit when one said elastic flexure or deformation of the membrane portion (7; 7') is of a degree at least equal to a substantially predetermined limit, to generate thereby second information or signalling, the second information or signalling being representative of at least one from among an excessive pressure of the fluid, an incorrect pressure measurement, and an anomalous state of the pressure sensor.