"In person" and "in-person" are both correct when the first phrase is used as an adverb and the second is used as an adjective.

Definitions and examples follow from several sources:

IN PERSON

Definition from Microsoft Word for Windows, Word 2003 reference databases:

"In person: personally rather than being represented by somebody or something else."

in person. WordNet® 3.0 © 2006 by Princeton University.

adverb: in the flesh; without involving anyone else; "I went there personally"; "he appeared in person"

Synonym

A synonym for "in person" is personally

in person. The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 1997 by The Christine Ammer 1992 Trust. Houghton Mifflin Company.

Also, in the flesh. In one's physical presence, as in He applied for the job in person, or I couldn't believe it, but there she was, in the flesh. The first expression dates from the mid-1500s. The variant, from the 1300s, was long used to allude to the bodily resurrection of Jesus, but later acquired its looser meaning. Charles Dickens has it in Our Mutual Friend (1865): "The minutes passing on, and no Mrs. W. in the flesh appearing."

IN-PERSON

in-person. WordNet® 3.0 © 2006 by Princeton University.

adjective: an appearance carried out personally in someone else's physical presence; "he carried out the negotiations in person"; "a personal appearance is an appearance by a person in the flesh"

Synonym

A synonym for "in-person" is personal.

PERSON

Dictionary.com Unabridged (v 1.1) Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.

Person - noun

Definitions

1. a human being, whether man, woman, or child: The table seats four persons.

2.a human being as distinguished from an animal or a thing.

3.Sociology. an individual human being, esp. with reference to his or her social relationships and behavioral patterns as conditioned by the culture.

4.Philosophy. a self-conscious or rational being.

5.the actual self or individual personality of a human being: You ought not to generalize, but to consider the person you are dealing with.

6.the body of a living human being, sometimes including the clothes being worn: He had no money on his person.

7.the body in its external aspect: an attractive person to look at.

8.a character, part, or role, as in a play or story.

9.an individual of distinction or importance.

10.a person not entitled to social recognition or respect.

11.Law. a human being (natural person) or a group of human beings, a corporation, a partnership, an estate, or other legal entity (artificial person or juristic person) recognized by law as having rights and duties.

12.Grammar. a category found in many languages that is used to distinguish between the speaker of an utterance and those to or about whom he or she is speaking. In English there are three persons in the pronouns, the first represented by I and we, the second by you, and the third by he, she, it, and they. Most verbs have distinct third person singular forms in the present tense, as writes; the verb be has, in addition, a first person singular form am.

13.Theology. any of the three hypostases or modes of being in the Trinity, namely the Father, the Son, and the Holy Ghost.

Idioms

1. be one's own person, to be free from restrictions, control, or dictatorial influence: Now that she's working, she feels that she's her own person.

2. in person, in one's own bodily presence; personally: Applicants are requested to apply in person.

-Synonyms

Person, individual, personage are terms applied to human beings. Person is the most general and common word: the average person. Individual views a person as standing alone or as a single member of a group: the characteristics of the individual; its implication is sometimes derogatory: a disagreeable individual. Personage is used (sometimes ironically) of an outstanding or illustrious person: We have a distinguished personage visiting us today.

-Usage note

See the words individual, party, people, they.