when a switch is open, does any current flow through the equipment connected to the switch?

Without knowing what the circuit attached to the switch looks like, all we can say is that no current is flowing through the switch (unless there is a very bright arc across its terminals). That does NOT mean that one (or both) terminals are not energized.

In addition to what Alan stated, in theory, no current can flow if the switch is open. However, in reality there is often some leakage current flowing through the ground or neutral connection.

if u talk about LV distribution circuits, it depends on the circuit configration and some times when we use 3 poles CBs on the 3 phase star connection we can sense some current on the netral wire due to the unblace 3 phase load.

Basically no current should flow in the equipment.

actually the answer is the switch is considered to be two metallic plates with a adjustment to interlink them...............
so when the switch is open it behaves like capacitor hence capacitive current flows.......

Pl remember you are assuning may things here 1) swicth is rated to handle the current 2) To sustain the voltage difference acroos the switch contact 3) When You are using term OPEN you mean mechanical position of the switch designated as OPEN
4) How accuarately youare able to measure current in circuit with switch in OPEN position 5) whether you are using in ac or in dc circuit,,, If off load switch is opened out while current is flowing through the same , it will continue arcing even in open position

No. There is a reason model electric codes, code authorities, OSHA, good facilities maintenance practices, etc., consider rigid lock-out, tag-out procedures one of the first foundations of safe practice. No measurable current should flow through a safe, properly operating switch that opens un-grounded conductors. If so, then there are either wiring or switch maintenance issues.

If the wiring is made in accordance with Electricity rules and codes, no current should flow through the equipment. The current should remain "Standby" at the disconnecting terminal of switch.

A "perfect" switch in the open position will have an infinite impedance and no current will flow through it. Depending on the system voltage and ambient conditions, you can expect some leakage current to pass through the "open" switch due to conductance through the air or contaminants, or through the capacitance between the switch contacts. If you have well maintained low voltage switchgear, in a clean, cool, and dry environment, leakage current will be virtually non-existent. If you have high voltage switchgear that is contaminated and is operating in hot, humid conditions, the leakage current through the switch will be high enough to draw an arc when service (safety) grounds are installed to create "an electrically safe condition" for maintenance workers. That's why safety grounds must be used when working on high voltage systems.

What is your definition of "any"? What else is connected to the "equipment"? On it's face your question is simplistic and the answer obvious, but I have to wonder if more is going on here.