If someone tried to break into my apartment, can I break my lease?

Unfortunately, under the circumstances you describe, you probably can't break your lease, at least not without a penalty. The law provides a tenant something called the "implied warranty of habitability," which means that the rental premises must be sanitary and safe (i.e. no leaking toilets, bugs, etc.). There is another protection called the "covenant of quiet enjoyment," which provides that tenants must be able to make use of their premises without undue disturbance. Either one could potentially be used as the basis for damages or to break a lease for safety related issues but only if the landlord is reponsible for them and has control over them. If it's simply that you believe that your rental is not in a safe neighborhood or the like, that is not the landlord's responsibility and it's not something he can control, then it's not a basis for breaking the lease. However, if your buildling is not secure to the outside so that strangers can walk the halls of the apartment complex or if your neighboring tenants are engaged in criminal activity, then you may have a claim. If you think that any of the foregoing applies, then you should consult directly with an attorney to see if you have good grounds to get out of your lease.

No, you can't break your lease because someone tried to break into your apartment. You can't even break it if someone does break in, or even if they assault you. The lease is a contract between you and the landlord. The landlord is not responsible for the actions of third parties, especially criminal acts by third parties. You can only break your lease without penalty if the *landlord* violates his or her obligations under the lease (or his or her implied obligations under the warranty of habitability or covenant of quiet enjoyment--basically, the landlord doesn't fix major health or habitability issues, like bad leaks, mold, heat, etc., or the landlord keeps disturbing you in your unit). If the landlord honors his or her obligations, then if you break the lease, you will be in breach of contract and the landlord could sue you for all rent remaining for the balance of the lease.