The crime is ...

... armed robbery.

Each word in the list ...

... is missing its first letter. There is an even number of words in each list and the (completed) words can be matched to form pairs. These pairs are common phrases that can be abbreviated by the (missing) initial letters, e.g. United Nations is abbreviated as UN. In some cases, the couple forms a single word, that is still abrreviated by the first two letters of the segments, e.g. centimetre is abbreviated as cm.

CM   CENTIMETṚE          PR   PUBLIC RẸLATIONS      CF   CARBỌN FIBER
OO   OḄJECT ORİENTED     IA   INTEṚ ALİA            AA   ALCOḢOLICS ANỌNYMOUS
UN   UṄITED NẠTIONS      SP   SERVİCE PROVỊDER      PR   PẸRSONAL RECOṘD
NE   NORṬHEAṠT           TI   TEX̣AS INSTRUṀENTS     TR   TḢEODORE ROOSEVẸLT
TY   THAṄK YOU           OE   OLḊ ENGLIṢH           AE   AMERIC̣AN EXPRESṠ
                         LR   LONG RANGĖ            IL   INTERṄET LỊNK
                                                    NL   NETHERLANḊS

 Each pair has one word with a dot above and one word with a dot below. Some headless words don't have dots, so they are probably on the missing letter. Other than helping to find pairs, I haven't found any significance to the dots, but perhaps I'm overlooking something here. Perhaps the dots are used in ordering the pairs?

Anyway, we can read the abbreviations column-wise and get the motive count money, the weapons pistol and rapier and the victim Captain Farrell.

These facts ...

... point to Whiskey in the Jar, an Irish folk song made popular by The Dubliners and other bands. There are slight variations in the lyrics in each interpretation, but the general plot is the same. Here's the first stanza:

    As I was a goin' over the far famed Kerry mountains
    I met with Captain Farrell and his money he was counting
    I first produced my pistol and I then produced my rapier
    Saying "Stand and deliver" for he were a bold deceiver

The crime is ...

... armed robbery.

Each word in the list ...

... is missing its first letter. There is an even number of words in each list and the (completed) words can be matched to form pairs. These pairs are common phrases that can be abbreviated by the (missing) initial letters, e.g. United Nations is abbreviated as UN. In some cases, the couple forms a single word, that is still abrreviated by the first two letters of the segments, e.g. centimetre is abbreviated as cm.

CM   CENTI-METṚE         PR   PUBLIC RẸLATIONS      CF   CARBỌN FIBER
OO   OḄJECT ORİENTED     IA   INTEṚ ALİA            AA   ALCOḢOLICS ANỌNYMOUS
UN   UṄITED NẠTIONS      SP   SERVİCE PROVỊDER      PR   PẸRSONAL RECOṘD
NE   NORṬH-EAṠT          TI   TEX̣AS INSTRUṀENTS     TR   TḢEODORE ROOSEVẸLT
TY   THAṄK YOU           OE   OLḊ ENGLIṢH           AE   AMERIC̣AN EXPRESṠ
                         LR   LONG RANGĖ            IL   INTERṄET LỊNK
                                                    NL   NETHER-LANḊS

  Each pair has one word with a dot above and one word with a dot below, but two words in each section don't have a dot. I didn't see the significance of the dots, but OP told me in the comments and now it's quite obvious to me: The dots determine the order of the pairs: Each dot below a letter lines up with a dot above a letter in the next line. (The hyphens are just there to enforce the alignment; I guess the alignment is also why the puzzle uses a monospace font.)

Anyway, we can read the abbreviations column-wise and get the motive count money, the weapons pistol and rapier and the victim Captain Farrell.

These facts ...

... point to Whiskey in the Jar, an Irish folk song made popular by The Dubliners and other bands. There are slight variations in the lyrics in each interpretation, but the general plot is the same. Here's the first stanza:

    As I was a goin' over the far famed Kerry mountains
    I met with Captain Farrell and his money he was counting
    I first produced my pistol and I then produced my rapier
    Saying "Stand and deliver" for he were a bold deceiver