Yes, you can.  But why would you?  Here is a great post provided by the Florida personal injury law firm of Perenich, Carroll, Perenich, Avril, Caulfield & Noyes, P.A. on this very topic:

The answer to this question really requires you to first answer this question: How important is the proper settlement of the claim to you?

If your answer is that the injury or its impact on you and your family require a proper settlement, then you should not deal directly with the insurance company on your own.

If you can easily say that the proper settlement is not important, then you may be able to try to settle the claim on your own. Even in this situation, however, there are some potential pitfalls that could lie in your path.

These pitfalls include the possibility that a release of one type of claim may actually release or impact other types of claims; a release may require the reimbursement of another insurance company for benefits paid; and a premature release may forever bar a later claim for more significant losses caused by a worsening condition. Because of these pitfalls and others you should almost always consult with an experienced attorney before attempting to settle a claim on your own.

One very specific example may help you understand why an attorney consultation is advisable.

John Smith, a Florida resident who has prudently purchased $100,000 in Uninsured Motorist Benefits as a part of his automobile insurance, settles his claim, on his own, against a careless driver for the driver’s policy limits of $10,000. John feels he has done the right thing because the driver’s insurance company assures him that there are no assets worth pursuing. John signs the release and cashes the $10,000 settlement draft.

Only then, after consulting with an attorney, does John realize that he has probably lost his right to make a claim against his own Uninsured Motorist Coverage above the $10,000 settlement. What John did not realize is that his insurance policy contained a provision requiring him not to sign the release.

Of course, if you feel the proper settlement of the claim is important to you it is critical that you not attempt to negotiate the matter on your own. There are many disadvantages that you have in dealing directly with an insurance company and many advantages that you gain in having an experienced attorney at your side.

The insurance company is in the business of settling claims for the lowest sum possible. It is also in the business of reducing the value of claims in a particular geographical area. Most importantly, it is in the business of developing evidence to defeat or minimize the value of your specific claim.

All of these “skills” of the insurance company work to your disadvantage in a negotiation process. While you are engaged in conversations with an apparently cooperative and pleasant claims adjustor the wheels are turning in the background to reduce the amount of your claim.

The insurance company’s objective is to keep you engaged in a dialogue long enough to give it the upper hand in the final negotiation. Statements are being taken from witnesses; photographs of the scene and of property damage are being obtained; surveillance videos may be in progress; if you provided signed medical authorizations to the adjustor, contact with the doctor and his staff is common.

Then, the actual negotiation process itself is likely to be a mismatch because you are talking to a person who negotiates for a living. You may be a fine carpenter or school teacher, but it is unlikely that you have the negotiating skills to match a professional negotiator. The adjustor uses this mismatch to his or her advantage. You are repeatedly confronted with strategies that the adjustor has practiced for years. The result is likely to be a settlement that favors the insurance company by a huge amount.

An attorney experienced in injury law has the ability to overcome your disadvantages in dealing with the adjustor and to properly prepare your side of the claim. With an attorney a thorough investigation of the facts of the accident or incident assures that favorable evidence is gathered and preserved. It also assures that avenues of financial recovery beyond the obvious ones are considered.

In addition, the experienced attorney is knowledgeable in the medical aspects of your claim and is able to monitor your care and to provide insight to you. As a result, the medical side of your claim (both in the past and in the future) is more fully presented to the insurance company.

An attorney also knows the categories of losses that can be presented for compensation beyond the medical circumstances and expenses. These include loss of the ability to earn money, loss of the services and companionship of a spouse, disability, inability to lead and enjoy a normal life, physical pain, and emotional suffering. The careful development and presentation of each relevant category of loss impacts the value of the total claim.

The insurance company well knows the difference in negotiating with an unrepresented private citizen and an experienced attorney. It also knows the difference between an attorney who does not take claims to court when negotiations fail and one who does. Having representation is important, but having respected, experienced representation is best.

As you can see, for the overwhelming majority of claims it is not advisable to attempt a resolution on your own. This is especially true when initial consultations with experienced attorneys are usually free and the ultimate fee arrangement, if an attorney is retained, is customarily a percentage of the recovery.

When a proper settlement is important to you it is vitally important that you consult with an attorney experienced in injury law before dealing with the insurance company.