The following list, from IRS Publication 521, tells you that security deposits are not a deductible moving expense.
"You can't deduct the following items as moving expenses.
Any part of the purchase price of your new home.
Car tags.
Driver's license.
Expenses of buying or selling a home (including closing costs, mortgage fees, and points).
Expenses of entering into or breaking a lease.
Home improvements to help sell your home.
Loss on the sale of your home.
Losses from disposing of memberships in clubs.
Mortgage penalties.
Pre-move househunting expenses.
Real estate taxes.
Refitting of carpet and draperies.
Return trips to your former residence.
Security deposits (including any given up due to the move).
Storage charges except those incurred in transit and for foreign moves".
