Input leakage current affect on CMOS multiplexer ( TMUX1208 )
How does input leakage current affect the output of a CMOS
  multiplexer.


If either your source or load are high impedance (resistance) then the leakage current (in or out) multiplied by that high resistance produces an error voltage on top of your signal voltage.


  I am working on a board that operates with the current range up to
  pico ampere


Tricky and likely to be "a fail" using conventional devices like the one you listed unless your source is AC with a known frequency that can be dragged from the spurious DC level and noise with a filter or lock-in amplifier.