Can I get the deductible that I am out of pocket from my leasing office for a theft that occurred due to a broken window about which I complained?

1) If you can show that the thief broke in through the loose window (i.e. the loose window must have caused the break-in), and that he/she did so after you had complained about to the landlord, and that the landlord had enough time, after your complaint, to have reasonably addressed the issue, then you probably can recover your deductible. In this case, the failure to address a legitimate security complaint in a timely manner is negligent, or unreasonably careless, and a violation of the landlord's duty to provide safely habitable space (security is a component of this), which would make the landlord liable. Of course, if the landord will not voluntarily pay your deductible, you'd have to sue, and be able to show when you complained, how the thief got access, etc.
2) As alluded to above, landlords have an obligation to provide security; this is part of the "implied warranty of habitability," which is the obligation, imposed by law, to provide rental space fit for its intended purposes (e.g. living in). In theory, a refusal to address security concerns can allow you to treat the lease as terminated by this breach. First you need to provide provable written notice of the issue; then you need to give the landlord a reasonable chance--and likely, another 1 - 2 notices as follow-ups--to "cure" or fix the condition; and only if they still fail to do so, can you treat the lease as terminated. There are three pitfalls, however, and if you can't get over these hurdles, you could be held liable for all the rent due for the balance of the lease:
a) First, the landlord is only responsible for, and you can only terminate the lease over, conditions under his/her control: so if the landlord provides "reasonable" (not perfect; just what the average reasonable landlord would do) security, you can't move out because the neighborhood is or has become dangerous.
b) Second, if the landlord fixes the problem, you can't move, no matter what happened earlier.
c) It's subjective, or a judgment call, as to what is reasonable security or not, or whether the landlord acting in a reasonable time to fix problems. If a judge feels the landlord did enough, you'd still be liable under the lease.

1) If you can show that the thief broke in through the loose window (i.e. the loose window must have caused the break-in), and that he/she did so after you had complained about to the landlord, and that the landlord had enough time, after your complaint, to have reasonably addressed the issue, then you probably can recover your deductible. In this case, the failure to address a legitimate security complaint in a timely manner is negligent, or unreasonably careless, and a violation of the landlord's duty to provide safely habitable space (security is a component of this), which would make the landlord liable. Of course, if the landord will not voluntarily pay your deductible, you'd have to sue, and be able to show when you complained, how the thief got access, etc.
2) As alluded to above, landlords have an obligation to provide security; this is part of the "implied warranty of habitability," which is the obligation, imposed by law, to provide rental space fit for its intended purposes (e.g. living in). In theory, a refusal to address security concerns can allow you to treat the lease as terminated by this breach. First you need to provide provable written notice of the issue; then you need to give the landlord a reasonable chance--and likely, another 1 - 2 notices as follow-ups--to "cure" or fix the condition; and only if they still fail to do so, can you treat the lease as terminated. There are three pitfalls, however, and if you can't get over these hurdles, you could be held liable for all the rent due for the balance of the lease:
a) First, the landlord is only responsible for, and you can only terminate the lease over, conditions under his/her control: so if the landlord provides "reasonable" (not perfect; just what the average reasonable landlord would do) security, you can't move out because the neighborhood is or has become dangerous.
b) Second, if the landlord fixes the problem, you can't move, no matter what happened earlier.
c) It's subjective, or a judgment call, as to what is reasonable security or not, or whether the landlord acting in a reasonable time to fix problems. If a judge feels the landlord did enough, you'd still be liable under the lease.