Yes. A lot of people assume a high floor and a clean kitchen put them out of reach, and then find droppings in a closet on the fourth floor. Here's why height helps less than you'd expect.
Mice are capable climbers on rough surfaces, but in an apartment building they rarely need to climb the outside at all. The building provides vertical routes inside the walls: plumbing stacks, heating risers, electrical and cable chases, elevator and trash chutes, and the gaps where those pass through each floor. A mouse that gets into the basement or a ground-floor unit can move between floors without ever being seen.
Often somewhat, because upper floors are further from the entry points at ground level and from the trash areas that feed a population. But "less likely" isn't "protected." Once a building has an established population, mice spread to wherever there is shelter and food, and the risers connect every floor.
Cleanliness reduces how attractive your apartment is and how long mice stay, and it's worth doing. It doesn't stop them arriving. Mice in a building are traveling for shelter and warmth as much as food — especially as the weather turns cold — and a clean unit with an open gap under the sink is still a warm, quiet space connected to the rest of the building. They also need very little: a few crumbs behind a stove or a bag of pet food is enough.
If you only find droppings in a bedroom closet or behind one appliance, that's a clue about the route, not reassurance about the size of the problem. Note where and when you find them. Activity concentrated near a pipe or a wall shared with a neighbor usually points straight at the entry.
Seal the openings inside your apartment with rodent-resistant material — metal mesh or similar, not foam alone — around pipes and behind appliances. Store food and pet food in hard containers. Report activity in writing to the building, because in a multi-unit building the population lives in the structure, and treatment in one apartment without addressing the building tends to move mice rather than remove them.
Who handles what in a rental depends on your lease and local rules. If the building is being treated and you're still seeing mice, ask whether neighboring units and the basement are part of the program and whether the entry points in your unit have been sealed.
Seeing mice in an apartment, or managing a building? Call (833) 767-2812.