All of the inputs of the ATTiny devices feed CMOS gates, and the output of a tristateable output driver. The exception is ADC inputs which also feed an RC circuit with about 100kΩ resistance in series with a 14pF capacitor.
In all cases, when configured as an input, the impedance will be very high - on the order of a few hundred MΩ. This means that very little current will flow by virtue of the design of CMOS inputs. The current might be on the order of a few nA.
When configured as an output, the current flowing out is limited by the internal resistance which from experience is in the order of 60Ω. If you configure a pin as an output and then try to drive it from another output (e.g. you set the pin high, and then short it to ground), the current will be limited by only this internal resistance - about 80mA flows which is way outside the spec of the ATTiny output drivers. Basically this is a bad thing to be doing.