Around 47 minutes into A Hard Day's Night, there's a scene in a dressing room where, among other events going on, a tailor is measuring Paul's shoulders. The Beatles' manager then tells them that they're wanted in the television studio, so Paul walks away and the tailor is left holding out his measuring tape. John goes up to him, says in a funny voice, "I now declare this bridge open," and cuts the tape with a scissors.
The first scene in Head is the actual opening of a bridge. After some initial set up, the mayor starts making a speech: "Ladies and gentlemen, I hereby dedicate this magnificent marvel of modern architecture, one of the largest suspended arch bridges in the world, to the people of-" at which point, Micky interrupts him by running through the ribbon he was about to cut.
While the Beatles (and A Hard Day's Night specifically) are an acknowledged influence on the Monkees, I don't know if the faint resemblance between these two scenes is anything more than coincidence. Neither scene is very significant in relation to the larger plot, and the "bridge opening" in A Hard Day's Night isn't even real.
