An anti-tamper assembly (40, 40a) is provided in order to sense the attempted removal of a body attached to a surface (17) by a fastener (36, 36a). The assembly (40, 40a) includes an anti-tamper access-blocking element (42, 42a) positioned in an anti-tamper position proximal to the fastener (36, 36a), along with an anti-tamper switch (44, 102) operably coupled with the element (42, 42a) in order to bias the switch (44, 102) to one switch condition. In the event that the element (42, 42a) is moved from its anti-tamper position, the switch (44, 102) moves to another switch condition, which generates an alarm signal. The assembly (40, 40a) may be used to protect an alarm section (16, 16a) forming a part of an alarm assembly (10, 10a). The section (16, 16a) includes a sensor or switch (64) operable to detect relative movement between first and second members such as a door (12) and doorframe (14). In one embodiment, a magnetically actuatable switch (42) is employed with a mating access-blocking element (42) in the form of a magnet. Alternately, a mechanically actuatable switch (102) having an actuating arm (104) may be used where the arm (104) engages access-blocking element (42a).