As per 2002 code:
210.52(B)(1) Receptacle Outlets Served. In the kitchen, pantry, breakfast room, dining room, or similar area of a dwelling unit, the two or more 20-ampere small-appliance branch circuits required by 210.11(C)(1) shall serve all receptacle outlets covered by 210.52(A) and (C) and receptacle outlets for refrigeration equipment.
Exception No. 1: In addition to the required receptacles specified by 210.52, switched receptacles supplied from a general-purpose branch circuit as defined in 210.70(A)(1), Exception No. 1, shall be permitted.
Exception No. 1 to 210.52(B)(1) permits switched receptacles supplied from general-purpose 15-ampere branch circuits to be located in kitchens, pantries, breakfast rooms, and similar areas. See 210.70(A) and Exhibit 210.25 for details.
Exception No. 2: The receptacle outlet for refrigeration equipment shall be permitted to be supplied from an individual branch circuit rated 15 amperes or greater.
Exception No. 2 to 210.52(B)(1) allows a choice for refrigeration equipment receptacle outlets located in a kitchen or similar area. An individual 15-ampere or larger branch circuit may serve this equipment, or it may be included in the 20-ampere small-appliance branch circuit. Refrigeration equipment is also exempt from the GFCI requirements of 210.8.
So no, one is not required per NEC. However, your local building codes could require a dedicated line to the fridge. And it would be wise to do so. Always check the local codes!
Also, remember that no circuit is allowed (anywhere) to pull over 80% of the rated load, so no 20A circuit can pull more than a total combined load of 16A. That's running load, not startup. Motors are rated at 125% of the complete protection, so you want a RLA and FLA of no more than 16 amps, and a startup of no more than 25 amps (on a 20A protection of a branch). So even though code allows you to split the kitchen circuits into a minimum of 2, and that the fridge can be on one, if the fridge in question pulls a FLA or a RLA of 16 amps, you must install a dedicated circuit, anyway.
Keep in mind that if you do the minimum of 2, 20A circuits, you might face the probability that both will be GFI protected, which isn't a good idea for a fridge. The motor and condensor will constantly trip it.
My suggestion is to always install a dedicated circuit for the refrigerator. It's an economical method to avoid costly frustrations in the future, unless you're doing an apartment where the owner knows the fridge will only draw a tiny amount of current and it won't be ground fault protected.
There's the 2002 code and my advice. PM me if you'd like more information, my friend. Remember, only a fool does the minimum, for he considers not the future.