Peter Falk, best known as star of TV's "Colombo," will star in Arthur Miller's new play, Mr. Peters' Connections, beginning previews Apr. 28 at Off-Broadway's Signature Theatre. Rehearsals began Apr. 1 for an opening May 17. Previews start Apr. 28.

Appearing with Falk will be Tari Signor (Death Defying Acts), Jeff Weiss, Erica Bradshaw, Kris Carr, Anne Jackson (Twice Around The Park), Alan Mozes and Daniel Oreskes. Designing the show are Teresa Snider-Stein (costumes), Beverly Emmons (lighting), Francis O'Connor (set) and Red Ramona (sound).

Due to strong ticket demand, the show's run was extended from a June 7 close to June 21. Spokesperson Candi Adams (of the James Morrison office) told Playbill On-Line the full extended run sold out in mid-March.

Falk, who began his New York stage career in 1956 with The Iceman Cometh, appeared frequently on Broadway before his run in "Columbo." Appearances include The Passion of Josef D. (as Joseph Stalin) in 1964 and Neil Simon's The Prisoner of Second Avenue in 1971.

The New York Times described Mr. Peters' Connections as "a combination fantasia, comedy and memory play about a former pilot trying to figure out what happened to his life," but a spokesperson for the production (from the James Morrison office) said Miller is still rewriting the play. No other casting has been finalized. Falk described Mr. Peters' Connections to Variety as "a hilarious comedy about an ex-fighter pilot from WWII -- who is now older than anyone he ever knew. He is mystified by the contemporary scene. For instance, 'Why would penile augmentation cost $4,400 and hymen reconstruction $400 less?'"

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Signature is devoting its entire 1997-98 season to the work of Miller, who won the Pulitzer Prize for Death of a Salesman. Miller's The American Clock opened the 1997-98 season in October, followed by two one-acts: I Can't Remember Anything and The Last Yankee, which ran through Feb. 8.

Miller was on hand for a Sept. 9, 1997 morning press conference at the recently constructed Signature space, 555 West 42nd St., as were artistic director Jim Houghton, architect Mitchell Kurtz and set designer E. David Cosier.

Amidst the clanging, whirring, banging and whizzing of workmen's tools, the three men (and, temporarily, Houghton's young son, Henry) took seats in the unfinished room, with invited press sitting opposite on wooden risers. Also onhand were cast members of the season's first show, The American Clock, beginning the first day of rehearsal at the Raw Space next door.

"We searched for four years," Houghton told the assembled, "and over 250 spaces for a home. We'd really wanted the Provincetown Playhouse but that fell through. Then we talked to Eric Krebs, who started doing renovation on this space a year ago. He asked if we were ready to continue the renovations and take over, so we did [for a 14-year lease]. Also helping was a $1.5 million capital campaign, $1 million of which was raised very quickly, thanks especially to the Laura Pels Foundation." 71 percent of the $1.5 million has now been raised, with a goal of Sept. 1988 set for the whole amount.

Architect Kurtz then pointed out the desired design for the space would pay particular attention to the size of the stage in relation to the 160 seats in the audience. "We want a lot of stage, a lot of art. It should be prominent and reach from your eyes to my eyes. It should feel like, `come on over, we're gonna read a play in my apartment tonight. That's the feel. Plus the notion of a library, a civic space. There will be several `walls of words' on display; words that will change every year.

"Insulation will also be important," added Kurtz, "so actors can use their full, dynamic range of voice." The space is 45' X 85' with an 22' grid height, equipped with air conditioning, wheelchair accessibility and concessions facility. Kurtz's other designs include those for New York Theatre Workshop, Playwrights Horizons and Arkansas Rep.

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In his closing remarks to the press conference assembled, Miller stressed that his early, best-known works were created in a different atmosphere t -ts on Broadway today. "The Group Theatre was so important to the process. People were engaged to create, and felt connected, to each other and to the same ideals. That doesn't happen overnight. Today we don't have `theatre,' we have `shows.' It's a crapshoot. Last time I was in a theatre they were pouring the concrete for the Mitzi Newhouse at Lincoln Center. But that, too, became commercial. I hope this place will have the same spiritual engagement of those early years."

Miller's other works include Death Of A Salesman and A View From The Bridge. The latter play is being revived by Broadway's Roundabout Theatre and recently moved to the Neil Simon Theatre for a reopening April 3.

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Founded in 1991, Signature Theatre Company spent its first six seasons focusing on the works of Lee Blessing, Romulus Linney, Edward Albee, Horton Foote, Adrienne Kennedy and Sam Shepard respectively. (One of the Foote plays premiered there, The Young Man From Atlanta, went on to receive the Pulitzer Prize and have a Broadway engagement.)

Three seasons ago, the company was housed at the (now vanished) 77-seat theatre at Kampo Cultural Center downtown. The last two seasons were at the Public Theatre space. Producer and owner of the West 42nd St. space, Krebs has stated, "Playwright John Ford Noonan said to me, `You know why I like Signature Theatre Company? -- They give working playwrights hope.'"

For memberships (starting at $90) and information on the Signature Theatre season call (212) 244-PLAY. As of Apr. 20, Signature had not yet selected a playwright to honor for its next season.

-- By David Lefkowitz