No, insider trading doesn't apply to private companies. By definition private companies don't trade their stock on the open market. Trading on the open market provides access to an immense pool of capital (anyone with the price of a share of stock), but the trade-off is that there are many more strictures on corporate behavior and governance. Private companies have far more latitude in their corporate governance, but on the other hand they are far more limited in who they can sell stock too, typically being limited to accredited investors.
It seems that in the US this answer is actually wrong, but the situation is complex. The SEC has sanctioned privately held companies under Rule 10b-5 for fraud and misrepresentation for stock transactions where material information was withheld from the other parties.
Stiefel Laboratories, a privately held firm, was charged with buying back employee shares without disclosing that it had multiple offers from private equity firms to purchase stock at a higher price, or revealing that it was in negotiations to sell the company to GlaxoSmithKline.